n° 152

harmonics in

industrial

networks

Pierre Roccia

Noël Quillon

Obtained an Electrical Engineering

degree from the INPG (National Polytechnic Institute of Grenoble) in 1969.

Worked as project manager in the

industrial equipment and high voltage public distribution sector, before

being put in charge of extending the

Merlin Gerin range of protection

relays and developing a technical

approach for the protection of high

voltage industrial networks using

devices associated with circuit

breakers.

After three years as a training

instructor, he is presently working as

an engineer in the "Network Studies"

department of the Central R&D

organisation.

After joining Merlin Gerin's Low

Voltage Equipment Department in

1968, he subsequently took part in

the development of LV circuit breakers within the testing laboratory.

A graduate engineer from the INPG,

he worked in the "Network Studied"

department of the Central R&D

organisation for eight years where he

studied electrical network phenomena and their behaviour in order to

establish guidelines to control these

phenomena. In 1985, he joined the

Training Department. After being in

charge of the electrotechnical training programme, he is presently the

training correspondent for the UPS

division.

E/CT 152 first issued october 1994

glossary

Symbols:

C

D

δ

f1

far

fn

fr

ϕn

In

j

L

Lsc

n

nar

nr

k

p

p1

pn

P (W)

PB

q

Q

Q (var)

r

R

spectrum

Ssc

T

U

Vn

X

X0

Xsc

Y0

Yn

Z

capacitance or, more generally, the capacitors themselves

harmonic distortion

loss angle of a capacitor

fundamental frequency

anti-resonance frequency

frequency of the nth harmonic component

resonance frequency

phase angle of the nth harmonic component when t = 0

rms current of the nth harmonic component

complex operator equal to the square root of −1

inductance or, more generally, the reactors, producing the inductance

short-circuit inductance of a network, seen from a given point, as defined by Thevenin's theorem

the order of a harmonic component (also referred to as the harmonic number)

the order of anti-resonance, i.e. the radio of the anti-resonance frequency to the fundamental frequency

the order of resonance, i.e. the radio of the resonance frequency to the fundamental frequency

a positive integer

number of rectifier arms (also referred to as the pulse number)

filter losses due only to the fundamental current

filter losses due only to the nth harmonic current

active power

pass-band of a resonant shunt filter

quality factor of a reactor

quality factor of a filter

reactive power

resistance

resistance (or the real part of the impedance)

the distribution, at a given point, of the amplitudes of the various harmonic components expressed relative to the

fundamental

short-circuit power of a network at a given point

period of an alternating quantity

phase-to-phase rms voltage

rms voltage of the nth harmonic component

reactance

characteristic inductance or impedance of a filter

short-circuit reactance of a network, seen from a given point, as defined by Thevenin's theorem

amplitude of the DC component

rms value of the nth harmonic component

impedance

Abbreviations:

CIGRE

Conférence Internationale des Grands Réseaux Electriques (International Conference on Large Electrical

Networks)

IEC

International Electrotechnical Commission

Cahier Technique Merlin Gerin n° 152 / p.2

harmonics in industrial networks

summary

1. Introduction: harmonic distortion is a problem that must often be

p. 4

dealt with in industrial power distribution networks

2. Harmonic quantities

p. 4

3. Principal disturbances caused by

Instantaneous effects

p. 6

harmonic currents and voltages

Long-term effects

p. 6

4. Acceptable limits, recommendations Typical limits for distribution

p. 7

and standards

networks

Typical limits for industrial

p. 7

networks

5. Harmonics generators

Static converters on 3-phase

p. 8

networks

Arc furnaces

p. 8

Lighting

p. 9

Saturated reactors

p. 9

Rotating machines

p. 9

Calculation model

p. 9

6. Can capacitors cause a problem on

In the absence of capacitor banks p. 10

networks comprising disturbing

In the presence of a capacitor

p. 10

equipment

bank

7. Anti-harmonic reactors

p. 13

8. Filters

Resonant shunt filters

p. 14

Damped filters

p. 15

9. Measurement relays required for the Basic protection against device p. 17

protection of reactor-connected

failures

capacitors and filters

Basic protection against abnormal p. 17

stresses on the devices

10. Example of the analysis of a

Capacitor bank alone

p. 18

simplified network

Reactor-connected capacitor bank p. 18

Resonant shunt filter tuned to the p. 19

5th harmonic and a damped filter

tuned to the 7th harmonic

11. Conclusion

p. 21

12. Bibliography

p. 22

Cahier Technique Merlin Gerin n° 152 / p.3

1. introduction

harmonic distortion is a

problem that must often be

dealt with in industrial

power distribution

networks

Electricity is generally distributed as

three voltage waves forming a 3-phase

sinusoidal system. One of the

characteristics of such a system is its

waveform, which must always remain

as close as possible to that of a pure

sine wave.

If distorted beyond certain limits, as is

often the case on networks comprising

sources of harmonic currents and

voltages such as arc furnaces, static

power converters, lighting systems,

etc., the waveform must be corrected.

The aim of the present document is to

provide a better understanding of these

harmonics problems, including their

causes and the most commonly used

solutions.

2. harmonic quantities

To help the reader follow the

discussion, we will first review the

definitions of a number of terms related

to harmonics phenomena. Readers

already familiar with the basic

terminology may proceed directly to the

next chapter.

On AC industrial power supply

networks, the variation of current and

voltage with time is considerably

different from that of a pure sine wave

(see fig. 1). The actual waveform is

composed of a number of sine waves

of different frequencies, including one

at the power frequency, referred to as

the fundamental component or simply

the «fundamental».

By definition, the harmonic order of the

fundamental f1 is equal to 1. Note that

the harmonic of order n is often referred

to simply as the nth harmonic.

Expression of the distorted wave

Any periodic phenomenon can be represented by a Fourier series as follows:

Spectrum

The spectrum is the distribution of the

amplitudes of the various harmonics as

a function of their harmonic number,

often illustrated in the form of a

histogram (see fig. 2).

y(t) = Y 0 + ∑ Y n 2 sin (nωt − ϕ n )

I phase

Cahier Technique Merlin Gerin n° 152 / p.4

fundamental

harmonic

t

Harmonic order

The harmonic order, also referred to as

the harmonic number, is the ratio of the

frequency fn of a harmonic to that of the

fundamental (generally the power

frequency, i.e. 50 or 60 Hz):

fn

.

f1

n = 1

where:

■ Y0 = the amplitude of the DC

component, which is generally zero in

electrical power distribution;

distorted wave

Harmonic component

The term «harmonic component», or

simply «harmonic», refers to any one of

the above-mentioned sinusoidal

components, the frequency of which is

a multiple of that of the fundamental.

The amplitude of a harmonic is

generally a few percent of that of the

fundamental.

n =

n = ∞

fig.1: shape of a distorted wave.

■ Yn = the rms value of the

nth harmonic component,

■ ϕn = phase angle of the nth harmonic

component when t = 0.

Harmonics with an order above 23 are

often negligible.

Rms value of a distorted wave

Harmonic quantities are generally

expressed in terms of their rms value

since the heating effect depends on this

value of the distorted waveform.

For a sinusoidal quantity, the rms value

is the maximum value divided by the

square root of 2.

For a distorted quantity, under steadystate conditions, the energy dissipated

by the Joule effect is the sum of the

energies dissipated by each of the

harmonic components:

R I 2 t = R I12 t + R I 22 t + ... + R I n2 t

where:

I 2 = I12 + I 22 + ... + I n2

i.e. where:

I =

n = ∞

∑

n = 1

I n2

if the resistance can be considered to

be constant.

The rms value of a distorted waveform

can be measured either directly by

instruments designed to measure the

true rms value, by thermal means or by

spectrum analysers.

Individual harmonic ratio and total

harmonic distortion

The industrial harmonic ratios and the

total harmonic distortion quantify the

harmonic disturbances present in a

power supply network.

■ individual harmonic ratio (or harmonic

percentage)

The harmonic ratio expresses the

magnitude of each harmonic with

respect to the fundamental (see fig. 2).

The nth harmonic ratio is the ratio of the

rms value of the nth harmonic to that of

the fundamental.

For example, the harmonic ratio of In is

In/I1 or 100 (In/I1) if expressed as a

percentage (note that here In is not the

nominal or rated current);

■ total harmonic distortion (also

referred to as THD, the total harmonic

factor or simply as distortion D).

The total harmonic distortion quantifies

the thermal effect of all the harmonics.

It is the ratio of the rms value of all the

harmonics to that of one of the two

following quantities (depending on the

definition adopted):

the fundamental (CIGRE), which can

give a very high value:

n = ∞

∑

D =

n = 2

Y1

Y n2

the measured rms quantity

(IEC 555-1), in which case 0 < D < 1:

n = ∞

∑

D =

n = 2

n = ∞

∑

n = 1

Y n2

Y n2

Unless otherwise indicated, we will use

the definition adopted by CIGRE (see

the glossary) which corresponds to the

ratio of the rms value of the harmonic

content to the undistorted current at

power frequency.

100 %

1

5

7

n

fig. 2: the amplitude of a harmonic is often

expressed with respect to that of the

fundamental.

Cahier Technique Merlin Gerin n° 152 / p.5

3. principal disturbances caused by

harmonic currents and voltages

Harmonic currents and voltages superimposed on the fundamental have combined effects on equipment and devices

connected to the power supply network.

The detrimental effects of these

harmonics depend on the type of load

encountered, and include:

■ instantaneous effects;

■ long-term effects due to heating.

instantaneous effects

Harmonic voltages can disturb

controllers used in electronic systems.

They can, for example, affect thyristor

switching conditions by displacing the

zero-crossing of the voltage wave (see

IEC 146-2 and Merlin Gerin «Cahier

Technique» n° 141).

Harmonics can cause additional errors in

induction-disk electricity meters. For

example, the error of a class 2 meter will

be increased by 0.3 % by a 5th harmonic

ratio of 5 % in current and voltage.

Ripple control receivers, such as the

relays used by electrical utilities for

centralised remote control, can be

disturbed by voltage harmonics with

frequencies in the neighbourhood of the

control frequency. Other sources of

disturbances affecting these relays,

related to the harmonic impedance of

the network, will be discussed further on.

Vibrations and noise

The electrodynamic forces produced by

the instantaneous currents associated

with harmonic currents cause vibrations

and acoustical noise, especially in

electromagnetic devices (transformers,

reactors, etc.).

Pulsating mechanical torque, due to

harmonic rotating fields, can produce

vibrations in rotating machines.

Interference on communication and

control circuits (telephone, control

and monitoring)

Disturbances are observed when

communication or control circuits are

run along side power distribution

circuits carrying distorted currents.

Parameters that must be taken into

account include the length of parallel

Cahier Technique Merlin Gerin n° 152 / p.6

running, the distance between the two

circuits and the harmonic frequencies

(coupling increases with frequency).

long-term effects

Over and above mechanical fatigue

due to vibrations, the main long-term

effect of harmonics is heating.

Capacitor heating

The losses causing heating are due to

two phenomena: conduction and

dielectricc hysteresis.

As a first approximation, they are

proportional to the square of the applied

voltage for conduction and to the

frequency for hysteresis.

Capacitors are therefore sensitive to

overloads, whether due to an

excessively high fundamental or to the

presence of voltage harmonics.

These losses are defined by the loss

angle δ of the capacitor, which is the

angle whose tangent is the ratio of the

losses to the reactive power produced

(see fig. 3). Values of around 10-4 may

be cited for tan δ. The heat produced

can lead to dielectric breakdown.

Heating due to additional losses in

machines and transformers

■ additional losses in the stators (copper

and iron) and principally in the rotors

(damping windings, magnetic circuits) of

machines caused by the considerable

differences in speed between the

harmonic inducing rotating fields and the

rotor. Note that rotor measurements

(temperature, induced currents) are

difficult if not impossible.

■ supplementary losses in transformers

due to the skin effect (increase in the

resistance of copper with frequency),

hysteresis and eddy currents (in the

magnetic circuit).

Heating of cables and equipment

Losses are increased in cables carrying

harmonic currents, resulting in

temperature rise. The causes of the

additional losses include:

■ an increase in the apparent

resistance of the core with frequency,

due to the skin effect;

an increase in dielectric losses in the

insulation with frequency, if the cable is

subjected to non-negligible voltage

distortion;

■ phenomena related to the proximity

of conductors with respect to metal

cladding and shielding earthed at both

ends of the cable, etc.

Calculations can be carried out as

described in IEC 287.

Generally speaking, all electrical

equipment (electrical switchboards)

subjected to voltage harmonics or

through which harmonic currents flow,

exhibit increased energy losses and

should be derated if necessary.

For example, a capacitor feeder cubicle

should be designed for a current equal

to 1.3 times the reactive compensation

current. This safety factor does not

however take into account the

increased heating due to the skin effect

in the conductors.

Harmonic distortion of currents and

voltages is measured using spectrum

analysers, providing the amplitude of

each component.

The rms value of the distorted current

(or voltage) may be assessed in any of

three ways:

■ measurement using a device

designed to give the true rms value,

■ reconstitution on the basis of the

spectrum provided by spectral analysis,

■ estimation from an oscilloscope

display.

■

δ

tan δ =

p

Q

Q

p

fig. 3: triangle relating to the capacitor

powers, (active (P), reactive (Q),

apparent (R)).

4. acceptable limits, recommendations and standards

General limits

■ synchronous machines: permissible

stator current distortion = 1.3 to 1.4 %;

■ asynchronous machines: permissible

stator current distortion = 1.5 to 3.5 %;

■ cables: permissible core-shielding

voltage distortion = 10 %;

■ power capacitors: current

distortion = 83 %, corresponding to an

overload of 30 % (1.3 times the rated

current); overvoltages can reach up to

10 % (see IEC 871-1, 931-1 and

HD 525.1S1);

■ sensitive electronics: 5 % voltage

distortion with a maximum individual

harmonic percentage of 3 % depending

on the equipment.

typical limits for

distribution networks

The French electrical utility, EDF,

considers that voltage distortion will not

exceed 5 % at the supply terminals as

long as each individual subscriber does

not exceed the following limits:

■ 1.6 % voltage distortion;

■ individual harmonic percentages of:

0.6 % for even voltage harmonics,

1 % for odd voltage harmonics.

The table in figure 4 lists typical

percentages observed for the various

voltage harmonics where:

■ low value = value likely to be found in

the vicinity of large disturbing loads and

associated with a low probability of

having disturbing effects;

■ high value = value rarely exceeded in

the network, and with a higher

probability of having disturbing effects.

typical limits for industrial

networks

It is generally accepted that industrial

network without any sensitive

equipment such as regulators,

programmable controllers, etc. can

accept up to 5 % voltage distortion.

This limit and the limits for the

individual harmonic ratios may be

different if sensitive equipment is

connected to the installation.

harmonic

order

low

value (%)

high

value (%)

2

1

1.5

3

1.5

2.5

4

0.5

1

5

5

6

6

0.2

0.5

7

4

5

8

< 0.2

9

0.8

10

< 0.2

11

2.5

12

< 0.2

13

2

14

< 0.2

15

< 0.3

16

< 0.2

17

1

18

< 0.2

19

0.8

20

< 0.2

21

< 0.2

22

< 0.2

23

0.5

1.5

3.5

3

2

1.5

1

fig. 4: individual voltage harmonic percentages measured in high voltage distribution networks.

Cahier Technique Merlin Gerin n° 152 / p.7

5. harmonics generators

In industrial applications, the main

types equipment that generate

harmonics are:

■ static converters;

■ arc furnaces;

■ lighting;

■ saturated reactors;

■ other equipment, such as rotating

machines which generate slot

harmonics (often negligible).

static converters on

3-phase networks

Rectifier bridges and, more generally,

static converters (made up of diodes

and thyristors) generate harmonics.

A Graetz bridge, for instance, requires

a rectangular pulsed AC current (see

fig. 5) to deliver a perfect DC current. In

spite of their different waveforms, the

currents upstream and downstream

from the delta-star connected

transformer have the same

characteristic harmonic components.

The characteristic harmonic

components of the current pulses

supplying rectifiers have the following

harmonic numbers n, with n = kp ± 1,

where:

■ k = 1, 2, 3, 4, 5...

■ p = number of rectifier arms, for

example:

Graetz bridge

p = 6,

6-pulse bridge

p = 6,

12-pulse bridge

p = 12.

Applying the formula, the p = 6

rectifiers cited above generate

harmonics 5, 7, 11, 13, 17, 19, 23 and

25, and the p = 12 rectifiers generate

harmonics 11, 13, 23 and 25.

The characteristic harmonics are all

odd-numbered and have, as a first

approximation, an amplitude of In = I1/n

where I1 is the amplitude of the

fundamental.

This means that I5 and I7 will have the

greatest amplitudes. Note that they can

be eliminated by using a 12-pulse

bridge (p = 12).

In practice, the current spectrum is

slightly different. New even and odd

harmonics, referred to as non-

Cahier Technique Merlin Gerin n° 152 / p.8

characteristic harmonics, of low

amplitudes, are created and the

amplitudes of the characteristic

harmonics are modified by several

factors including:

■ asymmetry;

■ inaccuracy in thyristor opening times;

■ switching times;

■ imperfect filtering.

For thyristor bridges, a displacement of

the harmonics as a function of the

thyristor phase angle may also be

observed.

Mixed thyristor-diode bridges generate

even harmonics. They are used only at

low ratings because the 2nd harmonic

produces serious disturbances and is

very difficult to eliminate.

Other power converters such as cycloconverters, dimmers, etc. have richer

and more variable spectra than

rectifiers. Note that they are

increasingly replaced by converters

using the PWM (Pulse Width

Modulation) technique. These devices

operate at high chopping frequencies

(20 to 50 kHz) and are generally

designed to generate only low levels of

harmonics.

The harmonic currents of several

converters combine vectorially at the

common supply busbars. Their phases

are generally unknown except for the

case of diode rectifiers. It is therefore

possible to attenuate the 5 th and 7 th

current harmonics using two equally

loaded 6-pulse diode bridges, if the

couplings of the two power supply

transformers are carefully chosen

(see fig. 6).

arc furnaces

Arc furnaces used in the steel industry

may be of the AC (see fig. 7) or

DC type.

AC arc furnaces

(see fig. 7)

The arc is non-linear, asymmetric and

unstable. It generates a spectrum

load

I

I

T

T

t

t

T/6

T/3

rectifier supply phase current

T/6

phase current upstream from a delta-star

connected transformer supplying the rectifier

fig. 5: alternating current upstream from a Graetz bridge rectifier delivering a perfect direct

current.

including odd and even harmonics as

was well as a continuous component

(background noise at all frequencies).

The spectrum depends on the type of

furnace, its power rating and the

operation considered (e.g. melting,

refining). Measurements are therefore

required to determine the exact

spectrum (see fig. 8).

DC arc furnaces

(see fig. 9)

The arc is supplied via a rectifier and is

more stable than the arc in AC furnaces.

The current drawn can be broken down

into:

■ a spectrum similar to that of a

rectifier;

■ a continuous spectrum lower than

that of an AC arc furnace.

To a large extent, the harmonic

currents drawn by the disturbing

equipment are independent of the other

loads and the overall network

impedance. These currents can

therefore be considered to be injected

into the network by the disturbing

equipment. It is simply necessary to

arbitrarily change the sign so that, for

calculation purposes, the disturbing

equipment can be considered as

current sources (see fig. 10).

The approximation is somewhat less

accurate for arc furnaces. In this case,

the current source model must be

corrected by adding a carefully selected

parallel impedance.

in %

In

I1

100

continuous spectrum

10

Lighting systems made up of discharge

lamps or fluorescent lamps are

generators of harmonic currents.

A 3rd harmonic ratio of 25 % is

observed in certain cases. The neutral

conductor then carries the sum of the

3rd harmonic currents of the three

phases, and may consequently be

subjected to dangerous overheating if

not adequately sized.

4

3.2

1.3

1

0.5

0.1

1

3

5

7

9 rang

fig. 8: current spectrum for an arc furnace

supplied by AC power.

HV

I5 and I7 attenuated

lighting

100

transformer

I5 and I7

I5 and I7

cable

Yy 0

Dy 11

rectifier

saturated reactors

The impedance of a saturable reactor is

varying with the current flowing

through it, resulting in considerable

current distortion. This is, for instance,

the case for transformers at no load,

subjected to a continuous overvoltage.

6-pulse

diode

bridge

6-pulse

diode

bridge

cable

load

load

furnace

equal loads

rotating machines

Rotating machines generate high order

slot harmonics, often of negligible

amplitude. However small synchronous

machines generate 3rd order voltage

harmonics than can have the following

detrimental effects:

■ continuous heating (without faults) of

earthing resistors of generator neutrals;

■ malfunctioning of current relays

designed to protect against insulation

faults.

calculation model

When calculating disturbances, static

converters and arc furnaces are

considered to be harmonic current

generators.

fig. 6: attenuation circuit for I5 and I7.

fig. 9: arc furnace supplied by DC power.

HV

transformer

Z

I

cable

furnace

fig. 7: arc furnace supplied by AC power.

fig. 10: harmonic current generators are

modelled as current sources.

Cahier Technique Merlin Gerin n° 152 / p.9

6. can capacitors cause a problem on networks

comprising disturbing equipment?

We will consider the two following

cases:

■ networks without power capacitors;

■ networks with power capacitors.

in the absence of capacitor

banks, harmonic

disturbances are limited

and proportional to the

currents of the disturbing

equipment.

In principle, in so far as are concerned

harmonics, the network remains

inductive.

Its reactance is proportional to the

frequency and, as a first estimate, the

effects of loads and resistance are

negligible. The impedance of the

network, seen from a network node, is

therefore limited to the short-circuit

reactance Xsc at the node considered.

The level of harmonic voltages can be

estimated from the power of the

disturbing equipment and the shortcircuit power at the node (busbars) to

which the disturbing equipment is

connected, the short-circuit reactance

considered to be proportional to the

frequency (see fig. 11).

In figure 11:

Lsc = the short-circuit inductance of the

network, seen from the busbars to

which the disturbing equipment is

connected,

In = currents of the disturbing

equipment,

Xsc n = Lsc ω n = Lsc n (2 π f1)

therefore

V n = Xsc n I n = Lsc n (2 π f1) I n.

The harmonic disturbances generally

remain acceptable as long as the

disturbing equipment does not exceed

a certain power level. However, this

must be considered with caution as

resonance (see the next section) may

be present, caused by a nearby

network possessing capacitors and

coupled via a transformer.

Cahier Technique Merlin Gerin n° 152 / p.10

Note: In reality, the harmonic

inductance of network X, without

capacitors (essentially a distribution

network), represented by Lsc, can only

be considered to be proportional to the

frequency in a rough approximation.

For this reason, the network shortcircuit impedance is generally

multiplied by a factor of 2 or 3 for the

calculations.

Therefore: Xn = k n X1 with k = 2 or 3.

The harmonic impedance of a network

is made up of different constituents

such as the short circuit impedance of

the distribution system as well as the

impedance of the cables, lines,

transformers, distant capacitors,

machines and other loads (lighting,

heating, etc.).

In

Vn

Xsc

I

fig. 11: the harmonic voltage Vn is

proportional to the current In injected by the

disturbing equipment.

node A (busbars)

in the presence of a

capacitor bank parallel

resonance can result in

dangerous harmonic

disturbances

Resonance exists between the

capacitor bank and the reactance of

the network seen from the bank

terminals.

The result is the amplification, with a

varying degree of damping, of the

harmonic currents and voltages if the

order of the resonance is the same as

that of one of the harmonic currents

injected by the disturbing equipment.

This amplified disturbance can be

dangerous to the equipment.

Lsc

I

In

0

a: harmonic electrical

representation of a phase.

E

50 Hz source

Lsc

node A (busbar)

This is a serious problem and will be

dealt with in below.

This phenomenon is referred to as

parallel resonance.

What is this parallel resonance and

how can it cause dangerous

harmonic disturbances?

In so far as harmonic frequencies are

concerned, and for a first

approximation, the network may be

represented as in figure 12.

Vn

load

C

C

load

disturbing equipment

b: single-line diagram.

fig. 12: equivalent diagrams for a circuit

subject to harmonic currents and including a

capacitor bank.

In this diagram:

Lsc = the short-circuit inductance of

the network seen from the busbars to

which the capacitor bank and the

disturbing equipment are connected,

C = capacitors,

In = currents of the disturbing

equipment,

load = loads (Joule effect,

transmission of mechanical energy).

In principle, we consider the shortcircuit harmonic reactance seen from

the busbars, i.e. the node (A) to which

the capacitors, the loads and the

disturbing equipment are connected,

giving Vn = ZAO In.

The impedance versus frequency

curves (see fig.13) show that:

■ for the resonance frequency far, the

inductive effect is compensated for

exactly by the capacitive effect;

■ the reactance of the rejecter circuit:

is inductive for low frequencies,

including the fundamental frequency,

increases with frequency, becoming

very high and suddenly capacitive at

the resonance frequency far;

■ the maximum impedance value

reached is roughly R = U2/P where P

represents the sum of the active power

values of the loaded motors, other than

those supplied by a static converter.

If a harmonic current In of order n , with

the same frequency as the parallel

resonance frequency far, is injected by

the disturbing equipment, the

corresponding harmonic voltage can be

estimated as Vn = R In

with n = n ar = f ar/f1.

Estimation of nar

The order nar of parallel resonance is

the ratio of the resonance frequency far

to the fundamental frequency f1 (power

frequency).

Consider the most elementary industrial

network, shown in the equivalent

diagram in figure 14, including a

capacitor bank C supplied by a

transformer with a short-circuit

inductance LT, where Lsc represents

the short-circuit inductance of the

distribution network seen from the

upstream terminals of the transformer,

f ar =

2π

1

.

(Lsc + L T ) C

The order of the parallel resonance is

roughly the same whether the network

impedance is seen from point A or

point B (e.g. the supply terminals).

In general, given the short-circuit power

at the capacitor bank terminals,

and undoubtedly present a danger to

the capacitors.

■ if the parallel resonance order

corresponds to the frequency of the

carrier-current control equipment of the

power distribution utility, there is a risk

of disturbing this equipment.

Ssc

Q

nar =

To prevent resonance from

becoming dangerous, it must be

forced outside the injected spectrum

and/or damped.

The short-circuit impedance of the

network is seldom accurately known

and, in addition, it can vary to a large

extent, thereby resulting in large

variations of the parallel resonance

frequency.

It is therefore necessary to stabilise this

frequency at a value that does not

correspond to the frequencies of the

injected harmonic currents. This is

achieved by connecting a reactor in

series with the capacitor bank.

where:

Ssc = short-circuit power at the

capacitor bank terminals,

Q = capacitor bank power at the

applied voltage.

Generally S is expressed in MVA and

Q in Mvar.

Practical consequences:

■ if the order of a harmonic current

injected by disturbing equipment

corresponds to the parallel resonance

order, there is a risk of harmonic

overvoltages, especially when the

network is operating at low loads. The

harmonic currents then become

intensively high in network constituents

XΩ

IZI Ω

~R

without capacitors

X = Lsc 2 π f

inductive

0

f (Hz)

without capacitors

IZI = Lsc 2 π f

0

f (Hz)

far

capacitive

far

fig. 13: curves showing the impedance due to the loads and due to the resistance of the

conductors.

B

A

LT

lopp

distributor

Lsc

load

C

I

0

fig. 14: the capacitor, together with the sum of the upstream impedances, forms a resonant

circuit.

Cahier Technique Merlin Gerin n° 152 / p.11

The rejecter circuit thus created is then

represented by the diagram in figure 15

where Vn = ZAO In.

A series resonance, between L and C,

appears. As opposed to this resonance,

which gives a minimum impedance, the

parallel resonance is often referred to

an anti-resonance.

The equation giving the frequency of

the anti-resonance is:

f ar =

1

(Lsc + L) C

2π

Lsc generally being small compared to

L, the equation shows that the

presence of reactor L, connected in

series with the capacitors, renders the

frequency far less sensitive to the

variations of the short-circuit inductance

Lsc (from the connections points =

busbars A).

Series resonance

The branch made up of reactor L and

capacitor C (see fig. 16), form a series

resonance system of impedance

Z = r + j(Lω - 1/Cω) with:

■ a minimum resistive value r

(resistance of the inductance coil) for

the resonance frequency fr;

■ a capacitive reactance below the

resonance frequency fr;

■ an inductive reactance above the

resonance frequency fr, where

fr =

1

2π

L C

.

The curves in figure 17 show the shape

of the network inductance, including the

short-circuit impedance and that of the

LC branch, seen from busbars A.

The choice of far depends on Lsc, L

and C, while that of fr depends only on

L and C; far and fr therefore become

closer as Lsc becomes small with

respect to L. The level of reactive

power compensation, and the voltage

applied to the capacitors, depend partly

on L and C.

The reactor L can be added in two

different manners, depending on the

position of the series resonance with

respect to the spectrum. The two forms

of equipment are:

■ anti-harmonic reactors (for series

resonance outside the spectrum lines);

■ filters (for series resonance on a

spectrum line).

XΩ

inductive

0

XΩ

ph1

f (Hz)

capacitive

inductive

fr

0

r

f (Hz)

far

capacitive

fr

busbar node, point A

IZIΩ

L

IZIΩ

L

Vn

Lsc

I

In

C

0

neutral

C

0

~r

r

f (Hz)

0

fig. 15: the reactor, connected in series with

the capacitor, forms a rejecter circuit.

Cahier Technique Merlin Gerin n° 152 / p.12

f (Hz)

fr

fig. 16: impedance of the rejecter circuit.

far

fig. 17: network impedance at point A.

fr

7. anti-harmonic reactors

An anti-harmonic reactor can be used

to protect a capacitor bank against

harmonic overloads. Such solutions are

often referred to as reactor-connected

capacitor installations.

The reference diagram is once again

figure 15.

In this assembly, the choice of L is such

that the LC branch (where L is the

reactor and C the reactive power

compensation capacitors) behaves

inductively for the harmonic

frequencies, over the spectrum.

As a result, the resonance frequency fr

of this branch will be below the

spectrum of the disturbing equipment.

The LC branch and the network (Lsc)

are then both inductive over the

spectrum and the harmonic currents

injected by the disturbing equipment

are divided in a manner inversely

proportional to the impedance.

Harmonic currents are therefore greatly

restricted in the LC branch, protecting

the capacitors, and the major part of

the harmonic currents flow in the rest of

the network, especially in the shortcircuit impedance.

The shape of the network impedance,

seen from the busbars to which the LC

branch is connected, is shown in

figure 18.

There is no anti-resonance inside the

current spectrum. The use of an antiharmonic reactor therefore offers two

advantages;

■ it eliminates the danger of high

harmonic currents in the capacitors;

■ it correlatively eliminates the high

distortions of the network voltage,

without however lowering them to a

specified low value.

Certain precautions are necessary:

■ no other capacitor banks must be

present that could induce, through antiresonance, a capacitive behaviour in

the initial network inside the spectrum;

■ care must be taken not to introduce

an anti-resonance with a frequency

used by the distribution utility for

carrier-current control, since this would

place an increased load on the high

frequency generators (175 Hz, 188 Hz).

The anti-harmonic reactor is tuned to

an order of 4.5 to 4.8, giving a value

of fr between 225 to 240 Hz for a

50 Hz network, which is very near the

ripple control frequency used on many

distribution networks;

■ due to the continuous spectrum, the

use of anti-harmonic reactors on arc

furnaces requires certain precautions

which can only be defined after carrying

out special studies.

IzIΩ

theoretical impedance without

the LC branch

f (Hz)

f1

fr

harmonic current

spectrum

far

fig. 18: the capacitors are protected when fr is well below the harmonic spectrum.

Cahier Technique Merlin Gerin n° 152 / p.13

8. filters

Filters are used when it is necessary to

limit harmonic voltages present on a

network to a specified low value. Two

types of filters may be used to reduce

harmonic voltages:

■ resonant shunt filters,

■ damped filters.

resonant shunt filters

The resonant shunt filter (see fig. 16) is

made up of an LC branch with a

frequency of

fr =

1

2π L C

tuned to the frequency of the voltage

harmonic to be eliminated.

This approach is therefore

fundamentally different than that of

reactor-connected capacitors

already described. At fr, the resonant

shunt presents a low minimum

impedance with respect to the

resistance r of the reactor. It therefore

absorbs nearly all the harmonic

currents of frequency fr injected, with

low harmonic voltage distortion (since

proportional to the product of the

resistance r and the current flowing in

the filter) at this frequency.

In principle, a resonant shunt is

installed for each harmonic to be

limited. They are connected to the

busbars for which harmonic voltage

reduction is specified. Together they

form a filter bank.

Figure 19 shows the harmonic

impedance of a network equipped with

a set of four filters tuned to the 5th, 7th,

11th and 13th harmonics. Note that

there are as many anti-resonances as

there are filters. These anti-resonances

must be tuned to frequencies between

the spectrum lines. A careful study must

therefore be carried out if it is judged

necessary to segment the filter bank.

Main characteristics of a resonant

shunt

The characteristics depend on

n r = fr/f1 the order of the filter tuning

frequency, with:

■ fr = tuning frequency;

■ f1 = fundamental frequency (generally

the power frequency, e.g. 50 Hz).

These characteristics are:

■ the reactive power for compensation:

Qvar.

The resonant shunt, behaving

capacitively below its tuning frequency,

contributes to the compensation of

reactive power at the power frequency.

The reactive power produced by the

shunt at the connection busbars, for an

operating voltage U1, is given by the

following equation:

Q var =

nr2

n12 −

U12 C 2π f1

n

(note that the subscript 1 refers to the

fundamental).

C is the phase-to-neutral capacitance

of one of the 3 branches of the filter

bank represented as a star.

At first glance, the presence of a

reactor would not be expected to

increase the reactive power supplied.

The reason is the increase in voltage at

power frequency f1 caused by the

inductance at the capacitor terminals;

■

characteristic impedance:

L

;

C

X0 =

the quality factor:

q = X0/r.

An effective filter must have a reactor

with a large quality factor q, therefore:

r << X0 at frequency fr.

Approximate values of q:

75 for air-cored reactors,

greater than 75 for iron-core reactors.

■ the pass-band (see fig. 20), in relative

terms:

■

PB =

f − fr

1

= 2

fr

q

=

r

;

X0

the resistance of the reactor:

r = X0/q.

This resistance is defined at

frequency fr.

It depends on the skin effect. It is also

the impedance when the resonant

shunt is tuned;

■ the losses due to the capacitive

current at the fundamental frequency:

■

p1 =

Q var

q nr

IZIΩ

IZIΩ

r

2

r

f

fr

1

5

7

fig. 19: impedance of a network equipped with shunt filters.

Cahier Technique Merlin Gerin n° 152 / p.14

11

13

f/f1

fig. 20: Z versus f curve for a resonant

shunt.

f (Hz)

with:

Qvar = reactive power for

compensation produced by the filter,

p1 = filter losses at power frequency

in W;

■ the losses due to the harmonic

currents cannot be expressed by simple

equations; they are greater than:

pn =

2

Unr

r

in which Unr is the phase-to-phase

harmonic voltage of order nr on the

busbars after filtering.

In practice, the performance of

resonant shunt filters is reduced by

mis-tuning and special solutions are

required as follows:

■ adjustment possibilities on the

reactors for correction of manufacturing

tolerances;

■ a suitable compromise between the q

factor and filter performance to reduce

the sensitivity to mis-tuning, thereby

accepting fluctuations of f1 (network

frequency) and fr (caused by the

temperature dependence of the

capacitance of the capacitors).

damped filters

2nd order damped filter

On arc furnaces, the resonant shunt

must be damped. This is because the

continuous spectrum of an arc furnace

increases the probability of an injected

current with a frequency equal to the

anti-resonance frequency. In this case, it

is no longer sufficient to reduce the

characteristic harmonic voltages. The

anti-resonance must also be diminished

by damping.

Moreover, the installation of a large

number of resonant shunts is often

costly, and it is therefore better to use a

wide-band filter possessing the following

properties:

■ anti-resonance damping;

■ reduced harmonic voltages for

frequencies greater than or equal to its

tuning frequency, leading to the name

«damped high-pass filter»;

■ fast damping of transients produced

when the filter is energised. The 2nd

order damped filter is made up of a

resonant shunt with a damping

resistor R added at the reactor

terminals. Figure 21 shows one of the

three phases of the filter.

The 2nd order damped filter has zero

reactance for a frequency fr higher than

the frequency f where:

f =

fr =

2π

1

and

L C

1+ Q q

2π q

(Q 2 − 1) L C

.

The filter is designed so that fr

coincides with the first characteristic

line of the spectrum to be filtered. This

line is generally the largest.

When Q (or R) take on high values, fr

tends towards f, which means that the

resonant shunt is a limiting case of the

2nd order damped filter.

It is important not to confuse Q, the

quality factor, with Qvar, the reactive

power of the filter for compensation.

The 2nd order damped filter operates

as follows:

■ below fr: the damping resistor

contributes to the reduction of the

network impedance at anti-resonance,

thereby reducing any harmonic

voltages;

■ at fr: the reduction of the harmonic

voltage to a specified value is possible

since, at this frequency, no resonance

can occur between the network and the

filter, the latter presenting an

impedance of a purely resistive

character.

However, this impedance being higher

than the resistance r of the reactor, the

filtering performance is less than for a

resonant shunt;

■ above fr: the filter presents an

inductive reactance of the same type as

the network (inductive), which lets it

adsorb, to a certain extent, the

spectrum lines greater than fr, and in

particular any continuous spectrum that

may be present. However, antiresonance, if present in the impedance

of the network without the filter, due to

the existing capacitor banks, reduces

the filtering performance. For this

reason, existing capacitor banks must

be taken into account in the design of

the network and, in some cases, must

be adapted.

The main electrical characteristics of a

2nd order damped filter depend on

n r = fr/f1 , the order of the filter tuning

frequency, with:

■ fr = tuning frequency;

■ f1 = fundamental frequency (generally

the power frequency, e.g. 50 Hz).

These characteristics are:

■ the reactive power for compensation:

For a 2nd order damped filter at

operating voltage U1 (the subscript 1

referring to the fundamental), the

reactive power is roughly the same as

for a resonant shunt with the same

inductance and capacitance, i.e. in

practice:

Q var =

nr2

2

nr − 1

U12 C 2π f1

C is the phase-to-neutral capacitance of

one of the 3 branches of the filter bank

represented as a star.

phase

XΩ

r

inductive

0

R

f (Hz)

L

capacitive

C

neutral

fr

f =

1

2π

L C

fig. 21: 2nd order damped filter.

Cahier Technique Merlin Gerin n° 152 / p.15

■

characteristic impedance:

X0 =

phase

L

;

C

the quality factor of the reactor:

q = X0/r

where r is the resistance of the reactor,

dependent on the skin effect and

defined at frequency fr;

■ the quality factor of the filter:

Q = R/X0.

The quality factors Q used are

generally between 2 and 10;

■ the losses due to the fundamental

compensation current and to the

harmonic currents; these are higher

than for a resonant shunt and can only

be determined through network

analysis.

The damped filter is used alone or in a

bank including two filters. It may also

be used together with a resonant shunt,

with the resonant shunt tuned to the

lowest lines of the spectrum.

Figure 22 compares the impedance of

a network with a 2nd order damped

filter to that of a network with a

resonant shunt.

■

Other types of damped filters

Although more rarely used, other

damped filters have been derived from

the 2nd order filter:

■ 3rd order damped filter (see fig. 23)

Of a more complex design than the 2nd

order filter, the 3rd order filter is

intended particularly for high

compensation powers.

The 3rd order filter is derived from a 2nd

order filter by adding another capacitor

bank C2 in series with the resistor R,

thereby reducing the losses due to the

fundamental.

C2 can be chosen to improve the

behaviour of the filter below the tuning

frequency as well, which favours the

reduction of anti-resonance.

The 3rd order filter should be tuned to

the lowest frequencies of the spectrum.

Given the complexity of the 3rd order

filter, and the resulting high cost, a 2nd

order filter is often preferred for

industrial applications;

■ type C damped filter (see fig. 24)

In this filter, the additional capacitor

bank C2 is connected in series with the

reactor. This filter offers characteristics

roughly the same as those of the 3rd

order filter;

Cahier Technique Merlin Gerin n° 152 / p.16

IZIΩ

r

with resonant shunt

R

Z

network

L

with 2nd order damped filter

C

f (Hz)

neutral

fig. 22: the impedance, seen from point A, of a network equipped with either a 2nd order

damped filter or a resonant shunt.

phase

phase

r

r

R

R

L

L

C2

C2

C

C

neutral

fig. 23: 3rd order damped filter.

■ damped double filter (see fig. 25)

Made up of two resonant shunts

connected by a resistor R, this filter is

specially suited to the damping of the

anti-resonance between the two tuning

frequencies;

low q resonant shunt

This filter, which behaves like a

damped wide-band filter, is designed

especially for very small installations

not requiring reactive power

compensation.

The reactor, with a very high

resistance (often due to the addition of

a series resistor) results in losses

which are prohibitive for industrial

applications.

neutral

fig. 24: type C damped filter.

phase

ra

rb

La

Lb

■

R

Cb

Ca

neutral

neutral

fig. 25: damped double filter.

9. measurement relays required for the protection of

reactor-connected capacitors and filters

An anti-harmonic reactor must

withstand the 3-phase short-circuit

current at the common reactorcapacitor terminals.

Furthermore, both anti-harmonic

reactors and filters must continuously

withstand fundamental and harmonic

currents, fundamental and harmonic

voltages, switching surges and

dielectric stresses.

In this chapter, anti-harmonic reactorconnected capacitor assemblies and

filters will be referred to collectively as

«devices».

basic protection against

device failures

All the elements of these devices can

be subject to insulation faults and shortcircuits, while the capacitor banks are

mainly the source of unbalance faults

caused by the failure of capacitor

elements.

■ protection of these devices against

insulation faults can be provided by

residual current relays (or zero phase

sequence relays).

Note:

the neutral is generally not distributed

on such devices;

for higher sensing accuracy, it is

better to use a toroidal type

transformer, encircling all the live

conductors of the feeder, rather than

three step-down current transformers;

■ protection against short-circuits can

be provided by overcurrent relays

installed on the «filter» feeder.

This protection must detect 2-phase

short-circuits at the common reactorcapacitor terminals, while letting

through inrush transients;

■ detection of unbalance currents in the

connections between the neutrals of

the double star connected capacitor

banks (see fig. 26).

In addition to the damage that can be

caused by the resulting unbalanced

stresses, the failure of a small number

of capacitor elements is detrimental to

filter performance.

This protection is therefore designed to

detect, depending on its sensitivity, the

failure of a small number of capacitor

elements. Of the single-pole type, this

protection must be:

insensitive to the harmonics,

set to above the natural unbalance

current of the double star connected

capacitor bank (this unbalance depends

on the accuracy of the capacitors),

set to below the unbalance current

due to the failure of a single capacitor

element,

operate on a major fault causing an

unbalance.

The fluctuation of the supply voltage

must be taken into account in the

calculation of all these currents.

basic protection against

abnormal stresses on the

devices

These abnormal stresses are

essentially due to overloads. To protect

against them, it is necessary to monitor

the rms value of the distorted current

(fundamental and harmonics) flowing in

the filter.

It is also necessary to monitor the

fundamental voltage of the power

supply using an overvoltage relay.

phase 1

current relay

C/2

phase 2

phase 3

r

r

r

L

L

L

C/2

C/2

C/2

C/2

C/2

fig. 26: unbalance detection for a double star connected capacitor bank.

Cahier Technique Merlin Gerin n° 152 / p.17

10. example of the analysis of a simplified network

The diagram in figure 27 represents a

simplified network comprising a

2,000 kVA six-pulse rectifier, injecting a

harmonic current spectrum, and the

following equipment which will be

considered consecutively in three

different calculations:

■ a single 1,000 kvar capacitor bank;

■ anti-harmonic reactor-connected

capacitor equipment rated 1000 kvar;

■ a set of two filters comprising a

resonant shunt tuned to the 5th

harmonic and a 2nd order damped filter

tuned to the 7th harmonic. The

capacitor bank implemented in this

manner is rated 1,000 kvar.

Note that:

■ the 1,000 kvar compensation power

is required to bring the power factor to

a conventional value;

■ the harmonic voltages already

present on the 20 kV distribution

network have been neglected for the

sake of simplicity.

This example will be used to compare

the performance of the three solutions,

however the results can obviously not

be applied directly to other cases.

capacitor bank alone

The network harmonic impedance

curve (see fig. 28), seen from the node

where the harmonic currents are

injected, exhibits a maximum (antiresonance) in the vicinity of the

7th current harmonic. This results in an

unacceptable individual harmonic

voltage distortion of 11 % for the 7th

harmonic (see fig. 29).

The following characteristics are also

unacceptable:

■ a total harmonic voltage distortion of

12.8 % for the 5.5 kV network,

compared to the maximum permissible

value of 5 % (without considering the

requirements of special equipment);

■ a total capacitor load of 1.34 times

the rms current rating, exceeding the

permissible maximum of 1.3

(see fig. 30).

The solution with capacitors alone is

therefore unacceptable.

Cahier Technique Merlin Gerin n° 152 / p.18

The network harmonic impedance

curve, seen from the node where the

harmonic currents are injected, exhibits

a maximum of 16 ohms (antiresonance) in the vicinity of

harmonic order 4.25. This unfortunately

favours the presence of 4th voltage

reactor-connected

capacitor bank

This equipment is arbitrarily tuned to

4.8 f1.

Harmonic impedance

(see fig. 31)

network

20 kV

Isc 12.5 kA

2,000 kVA

disturbing equipment

20/5.5 kV

5,000 kVA

Usc 7.5 %

Pcu 40 kW

5.5/0.4 kV

1,000 kVA

Usc 5 %

Pcu 12 kW

capa.

motor

load

reactor

+

capa.

560 kW

resonant shunt

and

2nd order damped filter

500 kVA at cos ϕ = 0.9

fig. 27: installation with disturbing equipment, capacitors and filters.

Z (Ω)

V (V)

38.2

350

11 %

7.75

H

fig. 28: harmonic impedance seen from the

node where the harmonic currents are

injected in a network equipped with a

capacitor bank alone.

3

5

7

8

9 10 11 13 H

fig. 29: harmonic voltage spectrum of a

5.5 kV network equipped with a capacitor

bank alone.

harmonic. However, the low

impedance, of an inductive character,

of the 5th harmonic favours the filtering

of the 5th harmonic quantities.

For the 20 kV network, the total

harmonic distortion is only 0.35 %, an

acceptable value for the distribution

utility.

Voltage distortion

(see fig. 32)

For the 5.5 kV network, the individual

harmonic voltage ratios of 1.58 %

(7th harmonic), 1.5 % (11th harmonic)

and 1.4 % (13th harmonic) may be too

high for certain loads. However in many

cases the total harmonic voltage

distortion of 2.63 % is acceptable.

Capacitor current load

(see fig. 33)

The total rms current load of the

capacitors, including the harmonic

currents, is 1.06 times the current rating,

i.e. less than the maximum of 1.3.

This is the major advantage of reactorconnected capacitors compared to the

first solution (capacitors alone).

I (A)

V (V)

50

1.55 %

- 82

48

1.5 % 45

1.4 %

19

0.6 %

3

5

7

8

9 10 11 13

fig. 30: spectrum of the harmonic currents

flowing in the capacitors for a network

equipped with a capacitor bank alone.

Z (Ω)

3

H

4

5

7

8

9

11 13 H

fig. 32: harmonic voltage spectrum of a

5.5 kV network equipped with reactorconnected capacitors.

resonant shunt filter tuned

to the 5th harmonic and a

damped filter tuned to the

7th harmonic

In this example, the distribution of the

reactive power between the two filters

is such that the filtered 5th and 7th

voltage harmonics have roughly the

same value. In reality, this is not

required.

Harmonic impedance

(see fig. 34)

The network harmonic impedance

curve, seen from the node where the

harmonic currents are injected, exhibits

a maximum of 9.5 ohms (antiresonance) in the vicinity of

harmonic 4.7.

For the 5th harmonic, this impedance is

reduced to the reactor resistance,

favouring the filtering of the 5th

harmonic quantities.

For the 7th harmonic, the low, purely

resistive impedance of the damped

filter also reduces the individual

harmonic voltage.

For harmonics higher than the tuning

frequency, the damped filter impedance

curve reduces the corresponding

harmonic voltages.

This equipment therefore offers an

improvement over the second solution

(reactor-connected capacitors).

I (A)

15.6

Z (Ω)

9.5

34

24 %

4.7

~ 4.25

4.8

H

fig. 31: harmonic impedance seen from the

node where the harmonic currents are

injected in a network equipped with reactorconnected capacitors.

5

7

11 13

H

fig. 33: spectrum of the harmonic currents

flowing in the capacitors for a network

equipped with reactor-connected

capacitors.

5

7

H

fig. 34: harmonic impedance seen from

the node where the harmonic currents

are injected in a network equipped with a

resonant shunt filter tuned to the

5th harmonic and a damped filter

tuned to the 7th harmonic.

Cahier Technique Merlin Gerin n° 152 / p.19

Voltage distortion

(see fig. 35)

For the 5.5 kV network, the individual

harmonic voltage ratios of 0.96 %,

0.92 %, 1.05 % and 1 % for the 5th,

7th, 11th and 13th harmonics

respectively are acceptable for most

sensitive loads. The total harmonic

voltage distortion is 1.96 %.

For the 20 kV network, the total

harmonic distortion is only 0.26 %, an

acceptable value for the distribution

utility.

Capacitor current load

The total rms current load of the

resonant shunt filter capacitors

(see fig. 36) is greater than 1.3 time the

current rating. The capacitance must

therefore be increased, which will

improve the filtering performance,

reducing the 5th harmonic ratio to less

than 1 %.

The result is of course an increase in

the reactive power compensation

capacity.

To avoid overcompensating, a compromise must be found for the size of

these capacitors. The calculation is

therefore repeated with this new data.

For the damped filter tuned to the 7th

harmonic, the total rms current load of

the capacitors (see fig. 37) is within the

tolerance of 1.3 times their current

rating.

This example demonstrates an initial

approach to the problem. However in

practice, over and above the

calculations relative to the circuit

elements (L, r, C and R), other

calculations are required before

I (A)

V (V)

0.96 %

0.91 %

1.05 %

1%

proceeding with the implementation of

any solution:

■ the spectra of the currents flowing in

the reactors connected to the

capacitors;

■ the total voltage distortion at the

capacitor terminals;

■ reactor manufacturing tolerances and

means for adjustment if necessary;

■ the spectra of the currents flowing in

the resistors of the damped filters and

their total rms value;

■ voltage and energy transients

affecting the filter elements during

energisation.

These more difficult calculations,

requiring a solid understanding of both

the network and the equipment, are

used to determine all the electrotechnical information required for the

filter manufacturing specifications.

I (A)

22

23 %

39

10

10 %

5

7

11 13

H

fig. 35: harmonic voltage spectrum of a

5.5 kV network equipped with a

resonant shunt filter tuned to the 5th

harmonic and a damped filter tuned to

the 7th harmonic.

Cahier Technique Merlin Gerin n° 152 / p.20

5

H

fig. 36: spectrum of the harmonic currents

flowing in the capacitors of a resonant shunt

filter tuned to the 5th harmonic on a network

equipped with a damped filter tuned to the

7th harmonic.

5

7

11 13

H

fig. 37: spectrum of the harmonic currents

flowing in the capacitors of a damped filter

tuned to the 7th harmonic on a network

equipped with a resonant shunt filter tuned

to the 5th harmonic.

11. conclusion

Static power converters are

increasingly used in industrial

distribution. The same is true for arc

furnaces in the growing electricpowered steel industry. All these loads

produce harmonic disturbances and

require compensation of the reactive

power they consume, leading to the

installation of capacitor banks.

Unfortunately these capacitors, in

conjunction with the inductances in the

network, can cause high frequency

oscillations that amplify harmonic

disturbances. Installers and operators

of industrial networks are thus often

confronted with a complex electrical

problem.

acquired experience, this document

should provide the necessary

background to, if not solve the

problems, at least facilitate discussions

with specialists.

The main types of harmonic

disturbances and the technical means

available to limit their extent have been

presented in this document. Without

offering an exhaustive study of the

phenomena involved or relating all

For further information or assistance,

feel free to contact the Network Studies

department of the Central R&D organisation of Merlin Gerin, a group of

specialised engineers with more than

twenty years of experience in this field.

Cahier Technique Merlin Gerin n° 152 / p.21

12. bibliography

Standards

■ IEC 146: Semi-conductor converters.

■ IEC 287: Calculation of the

continuous current rating of cables.

■ IEC 555-1: Disturbances in supply

systems caused by household

appliances and similar electrical

equipment - Definitions.

■ IEC 871-1 and HD 525.1-S-T:

Shunt capacitors for AC power systems

having a rated voltage above 660 V.

■ NF C 54-100.

■ HN 53 R01 (May 1981): EDF general

orientation report. Particular aspects

concerning the supply of electrical

power to sensitive electronic equipment

and computers.

Merlin Gerin's Cahier Technique

■ Residual current devices

Cahier Technique n° 114

R. CALVAS

■ Les perturbations électriques en BT

Cahier Technique n° 141

R. CALVAS

Other publications

■ Direct current transmission, volume 1

E. W. KIMBARK

published by: J. WILEY and SONS.

Le cyclo-convertisseur et ses

influences sur les réseaux

d'alimentation (The cyclo-converter and

its effects on power supply networks

T. SALZAM and W. SCHULTZ - AIM

Liège CIRED 75.

■

Perturbations réciproques des

équipements électroniques de

puissance et des réseaux - Quelques

aspects de la pollution des réseaux par

les distorsions harmoniques de la

clientèle (Mutual disturbances between

power electronics equipment and

networks - Several aspects concerning

network pollution by harmonic distortion

produced by subscribers).

Michel LEMOINE - DER EDF

RGE T 85 n° 3 03/76.

■

Cahier Technique Merlin Gerin n° 152 / p.22

■ Perturbations des réseaux industriels

et de distribution. Compensation par

procédés statistiques.

Résonances en présence des

harmoniques créés par les

convertisseurs de puissance et les

fours à arc associés à des dispositifs

de compensation.

(Disturbances on industrial and

distribution networks. Compensation by

statistical processes.

Resonance in the presence of

harmonics created by power converters

and arc furnaces associated with

compensation equipment.)

Michel LEMOINE - DER EDF

RGE T 87 n° 12 12/78.

■ Perturbations des réseaux industriels

et de distribution. Compensation par

procédés statistiques.

Perturbations de tension affectant le

fonctionnement des réseaux fluctuations brusques, flicker,

déséquilibres et harmoniques.

(Disturbances on industrial and

distribution networks. Compensation by

statistical processes.

Voltage disturbances affecting network

operation - fluctuations, flicker,

unbalances and harmonics.

M. CHANAS - SER-DER EDF

RGE T 87 n° 12 12/78.

■ Pollution de la tension

(Voltage disturbances).

P. MEYNAUD - SER-DER EDF

RGE T 89 n° 9 09/80.

■ Harmonics, characteristic

parameters, methods of study,

estimates of existing values in the

network.

(ELECTRA) CIGRE 07/81.

■ Courants harmoniques dans les

redresseurs triphasés à commutation

forcée.

(Harmonic currents in forced

commutation 3-phase rectifiers)

W. WARBOWSKI

CIRED 81.

Origine et nature des perturbations

dans les réseaux industriels et de

distribution.

(Origin and nature of disturbances in

industrial and distribution networks).

Guy BONNARD - SER-DER-EDF

RGE 1/82.

■ Problèmes particuliers posés par

létude du phénomène de distorsion

harmonique dans les réseaux.

(Particular problems posed by the study

of harmonic distortion phenomena in

networks).

P. REYMOND

CIGRE Study Committee 36 09/82.

■ Réduction des perturbations

électriques sur le réseau avec le four à

arc en courant continu (Reduction of

electrical network disturbances by DC

arc furnaces).

G. MAURET, J. DAVENE

IRSID SEE LYON 05/83.

■ Line harmonics of converters with DC

motor loads.

A. DAVID GRAHAM and EMIL T.

SCHONHOLZER.

IEEE transactions on industry

applications.

Volume IA 19 n° 1 02/83.

■ Filtrage dharmoniques et

compensation de puissance réactive Optimisation des installations de

compensation en présence

d'harmoniques.

(Harmonic filtering and reactive power

compensation - Optimising

compensation installations in the

presence of harmonics).

P. SGARZI and S. THEOLERE,

SEE Seminar RGE n° 6 06/88.

■

Cahier Technique Merlin Gerin n° 152 / p.23

Réal. : Illustration Technique Lyon -

Cahier Technique Merlin Gerin n° 152 / p.24

DTE - 10/94 - 2500 - Imprimeur :

harmonics in

industrial

networks

Pierre Roccia

Noël Quillon

Obtained an Electrical Engineering

degree from the INPG (National Polytechnic Institute of Grenoble) in 1969.

Worked as project manager in the

industrial equipment and high voltage public distribution sector, before

being put in charge of extending the

Merlin Gerin range of protection

relays and developing a technical

approach for the protection of high

voltage industrial networks using

devices associated with circuit

breakers.

After three years as a training

instructor, he is presently working as

an engineer in the "Network Studies"

department of the Central R&D

organisation.

After joining Merlin Gerin's Low

Voltage Equipment Department in

1968, he subsequently took part in

the development of LV circuit breakers within the testing laboratory.

A graduate engineer from the INPG,

he worked in the "Network Studied"

department of the Central R&D

organisation for eight years where he

studied electrical network phenomena and their behaviour in order to

establish guidelines to control these

phenomena. In 1985, he joined the

Training Department. After being in

charge of the electrotechnical training programme, he is presently the

training correspondent for the UPS

division.

E/CT 152 first issued october 1994

glossary

Symbols:

C

D

δ

f1

far

fn

fr

ϕn

In

j

L

Lsc

n

nar

nr

k

p

p1

pn

P (W)

PB

q

Q

Q (var)

r

R

spectrum

Ssc

T

U

Vn

X

X0

Xsc

Y0

Yn

Z

capacitance or, more generally, the capacitors themselves

harmonic distortion

loss angle of a capacitor

fundamental frequency

anti-resonance frequency

frequency of the nth harmonic component

resonance frequency

phase angle of the nth harmonic component when t = 0

rms current of the nth harmonic component

complex operator equal to the square root of −1

inductance or, more generally, the reactors, producing the inductance

short-circuit inductance of a network, seen from a given point, as defined by Thevenin's theorem

the order of a harmonic component (also referred to as the harmonic number)

the order of anti-resonance, i.e. the radio of the anti-resonance frequency to the fundamental frequency

the order of resonance, i.e. the radio of the resonance frequency to the fundamental frequency

a positive integer

number of rectifier arms (also referred to as the pulse number)

filter losses due only to the fundamental current

filter losses due only to the nth harmonic current

active power

pass-band of a resonant shunt filter

quality factor of a reactor

quality factor of a filter

reactive power

resistance

resistance (or the real part of the impedance)

the distribution, at a given point, of the amplitudes of the various harmonic components expressed relative to the

fundamental

short-circuit power of a network at a given point

period of an alternating quantity

phase-to-phase rms voltage

rms voltage of the nth harmonic component

reactance

characteristic inductance or impedance of a filter

short-circuit reactance of a network, seen from a given point, as defined by Thevenin's theorem

amplitude of the DC component

rms value of the nth harmonic component

impedance

Abbreviations:

CIGRE

Conférence Internationale des Grands Réseaux Electriques (International Conference on Large Electrical

Networks)

IEC

International Electrotechnical Commission

Cahier Technique Merlin Gerin n° 152 / p.2

harmonics in industrial networks

summary

1. Introduction: harmonic distortion is a problem that must often be

p. 4

dealt with in industrial power distribution networks

2. Harmonic quantities

p. 4

3. Principal disturbances caused by

Instantaneous effects

p. 6

harmonic currents and voltages

Long-term effects

p. 6

4. Acceptable limits, recommendations Typical limits for distribution

p. 7

and standards

networks

Typical limits for industrial

p. 7

networks

5. Harmonics generators

Static converters on 3-phase

p. 8

networks

Arc furnaces

p. 8

Lighting

p. 9

Saturated reactors

p. 9

Rotating machines

p. 9

Calculation model

p. 9

6. Can capacitors cause a problem on

In the absence of capacitor banks p. 10

networks comprising disturbing

In the presence of a capacitor

p. 10

equipment

bank

7. Anti-harmonic reactors

p. 13

8. Filters

Resonant shunt filters

p. 14

Damped filters

p. 15

9. Measurement relays required for the Basic protection against device p. 17

protection of reactor-connected

failures

capacitors and filters

Basic protection against abnormal p. 17

stresses on the devices

10. Example of the analysis of a

Capacitor bank alone

p. 18

simplified network

Reactor-connected capacitor bank p. 18

Resonant shunt filter tuned to the p. 19

5th harmonic and a damped filter

tuned to the 7th harmonic

11. Conclusion

p. 21

12. Bibliography

p. 22

Cahier Technique Merlin Gerin n° 152 / p.3

1. introduction

harmonic distortion is a

problem that must often be

dealt with in industrial

power distribution

networks

Electricity is generally distributed as

three voltage waves forming a 3-phase

sinusoidal system. One of the

characteristics of such a system is its

waveform, which must always remain

as close as possible to that of a pure

sine wave.

If distorted beyond certain limits, as is

often the case on networks comprising

sources of harmonic currents and

voltages such as arc furnaces, static

power converters, lighting systems,

etc., the waveform must be corrected.

The aim of the present document is to

provide a better understanding of these

harmonics problems, including their

causes and the most commonly used

solutions.

2. harmonic quantities

To help the reader follow the

discussion, we will first review the

definitions of a number of terms related

to harmonics phenomena. Readers

already familiar with the basic

terminology may proceed directly to the

next chapter.

On AC industrial power supply

networks, the variation of current and

voltage with time is considerably

different from that of a pure sine wave

(see fig. 1). The actual waveform is

composed of a number of sine waves

of different frequencies, including one

at the power frequency, referred to as

the fundamental component or simply

the «fundamental».

By definition, the harmonic order of the

fundamental f1 is equal to 1. Note that

the harmonic of order n is often referred

to simply as the nth harmonic.

Expression of the distorted wave

Any periodic phenomenon can be represented by a Fourier series as follows:

Spectrum

The spectrum is the distribution of the

amplitudes of the various harmonics as

a function of their harmonic number,

often illustrated in the form of a

histogram (see fig. 2).

y(t) = Y 0 + ∑ Y n 2 sin (nωt − ϕ n )

I phase

Cahier Technique Merlin Gerin n° 152 / p.4

fundamental

harmonic

t

Harmonic order

The harmonic order, also referred to as

the harmonic number, is the ratio of the

frequency fn of a harmonic to that of the

fundamental (generally the power

frequency, i.e. 50 or 60 Hz):

fn

.

f1

n = 1

where:

■ Y0 = the amplitude of the DC

component, which is generally zero in

electrical power distribution;

distorted wave

Harmonic component

The term «harmonic component», or

simply «harmonic», refers to any one of

the above-mentioned sinusoidal

components, the frequency of which is

a multiple of that of the fundamental.

The amplitude of a harmonic is

generally a few percent of that of the

fundamental.

n =

n = ∞

fig.1: shape of a distorted wave.

■ Yn = the rms value of the

nth harmonic component,

■ ϕn = phase angle of the nth harmonic

component when t = 0.

Harmonics with an order above 23 are

often negligible.

Rms value of a distorted wave

Harmonic quantities are generally

expressed in terms of their rms value

since the heating effect depends on this

value of the distorted waveform.

For a sinusoidal quantity, the rms value

is the maximum value divided by the

square root of 2.

For a distorted quantity, under steadystate conditions, the energy dissipated

by the Joule effect is the sum of the

energies dissipated by each of the

harmonic components:

R I 2 t = R I12 t + R I 22 t + ... + R I n2 t

where:

I 2 = I12 + I 22 + ... + I n2

i.e. where:

I =

n = ∞

∑

n = 1

I n2

if the resistance can be considered to

be constant.

The rms value of a distorted waveform

can be measured either directly by

instruments designed to measure the

true rms value, by thermal means or by

spectrum analysers.

Individual harmonic ratio and total

harmonic distortion

The industrial harmonic ratios and the

total harmonic distortion quantify the

harmonic disturbances present in a

power supply network.

■ individual harmonic ratio (or harmonic

percentage)

The harmonic ratio expresses the

magnitude of each harmonic with

respect to the fundamental (see fig. 2).

The nth harmonic ratio is the ratio of the

rms value of the nth harmonic to that of

the fundamental.

For example, the harmonic ratio of In is

In/I1 or 100 (In/I1) if expressed as a

percentage (note that here In is not the

nominal or rated current);

■ total harmonic distortion (also

referred to as THD, the total harmonic

factor or simply as distortion D).

The total harmonic distortion quantifies

the thermal effect of all the harmonics.

It is the ratio of the rms value of all the

harmonics to that of one of the two

following quantities (depending on the

definition adopted):

the fundamental (CIGRE), which can

give a very high value:

n = ∞

∑

D =

n = 2

Y1

Y n2

the measured rms quantity

(IEC 555-1), in which case 0 < D < 1:

n = ∞

∑

D =

n = 2

n = ∞

∑

n = 1

Y n2

Y n2

Unless otherwise indicated, we will use

the definition adopted by CIGRE (see

the glossary) which corresponds to the

ratio of the rms value of the harmonic

content to the undistorted current at

power frequency.

100 %

1

5

7

n

fig. 2: the amplitude of a harmonic is often

expressed with respect to that of the

fundamental.

Cahier Technique Merlin Gerin n° 152 / p.5

3. principal disturbances caused by

harmonic currents and voltages

Harmonic currents and voltages superimposed on the fundamental have combined effects on equipment and devices

connected to the power supply network.

The detrimental effects of these

harmonics depend on the type of load

encountered, and include:

■ instantaneous effects;

■ long-term effects due to heating.

instantaneous effects

Harmonic voltages can disturb

controllers used in electronic systems.

They can, for example, affect thyristor

switching conditions by displacing the

zero-crossing of the voltage wave (see

IEC 146-2 and Merlin Gerin «Cahier

Technique» n° 141).

Harmonics can cause additional errors in

induction-disk electricity meters. For

example, the error of a class 2 meter will

be increased by 0.3 % by a 5th harmonic

ratio of 5 % in current and voltage.

Ripple control receivers, such as the

relays used by electrical utilities for

centralised remote control, can be

disturbed by voltage harmonics with

frequencies in the neighbourhood of the

control frequency. Other sources of

disturbances affecting these relays,

related to the harmonic impedance of

the network, will be discussed further on.

Vibrations and noise

The electrodynamic forces produced by

the instantaneous currents associated

with harmonic currents cause vibrations

and acoustical noise, especially in

electromagnetic devices (transformers,

reactors, etc.).

Pulsating mechanical torque, due to

harmonic rotating fields, can produce

vibrations in rotating machines.

Interference on communication and

control circuits (telephone, control

and monitoring)

Disturbances are observed when

communication or control circuits are

run along side power distribution

circuits carrying distorted currents.

Parameters that must be taken into

account include the length of parallel

Cahier Technique Merlin Gerin n° 152 / p.6

running, the distance between the two

circuits and the harmonic frequencies

(coupling increases with frequency).

long-term effects

Over and above mechanical fatigue

due to vibrations, the main long-term

effect of harmonics is heating.

Capacitor heating

The losses causing heating are due to

two phenomena: conduction and

dielectricc hysteresis.

As a first approximation, they are

proportional to the square of the applied

voltage for conduction and to the

frequency for hysteresis.

Capacitors are therefore sensitive to

overloads, whether due to an

excessively high fundamental or to the

presence of voltage harmonics.

These losses are defined by the loss

angle δ of the capacitor, which is the

angle whose tangent is the ratio of the

losses to the reactive power produced

(see fig. 3). Values of around 10-4 may

be cited for tan δ. The heat produced

can lead to dielectric breakdown.

Heating due to additional losses in

machines and transformers

■ additional losses in the stators (copper

and iron) and principally in the rotors

(damping windings, magnetic circuits) of

machines caused by the considerable

differences in speed between the

harmonic inducing rotating fields and the

rotor. Note that rotor measurements

(temperature, induced currents) are

difficult if not impossible.

■ supplementary losses in transformers

due to the skin effect (increase in the

resistance of copper with frequency),

hysteresis and eddy currents (in the

magnetic circuit).

Heating of cables and equipment

Losses are increased in cables carrying

harmonic currents, resulting in

temperature rise. The causes of the

additional losses include:

■ an increase in the apparent

resistance of the core with frequency,

due to the skin effect;

an increase in dielectric losses in the

insulation with frequency, if the cable is

subjected to non-negligible voltage

distortion;

■ phenomena related to the proximity

of conductors with respect to metal

cladding and shielding earthed at both

ends of the cable, etc.

Calculations can be carried out as

described in IEC 287.

Generally speaking, all electrical

equipment (electrical switchboards)

subjected to voltage harmonics or

through which harmonic currents flow,

exhibit increased energy losses and

should be derated if necessary.

For example, a capacitor feeder cubicle

should be designed for a current equal

to 1.3 times the reactive compensation

current. This safety factor does not

however take into account the

increased heating due to the skin effect

in the conductors.

Harmonic distortion of currents and

voltages is measured using spectrum

analysers, providing the amplitude of

each component.

The rms value of the distorted current

(or voltage) may be assessed in any of

three ways:

■ measurement using a device

designed to give the true rms value,

■ reconstitution on the basis of the

spectrum provided by spectral analysis,

■ estimation from an oscilloscope

display.

■

δ

tan δ =

p

Q

Q

p

fig. 3: triangle relating to the capacitor

powers, (active (P), reactive (Q),

apparent (R)).

4. acceptable limits, recommendations and standards

General limits

■ synchronous machines: permissible

stator current distortion = 1.3 to 1.4 %;

■ asynchronous machines: permissible

stator current distortion = 1.5 to 3.5 %;

■ cables: permissible core-shielding

voltage distortion = 10 %;

■ power capacitors: current

distortion = 83 %, corresponding to an

overload of 30 % (1.3 times the rated

current); overvoltages can reach up to

10 % (see IEC 871-1, 931-1 and

HD 525.1S1);

■ sensitive electronics: 5 % voltage

distortion with a maximum individual

harmonic percentage of 3 % depending

on the equipment.

typical limits for

distribution networks

The French electrical utility, EDF,

considers that voltage distortion will not

exceed 5 % at the supply terminals as

long as each individual subscriber does

not exceed the following limits:

■ 1.6 % voltage distortion;

■ individual harmonic percentages of:

0.6 % for even voltage harmonics,

1 % for odd voltage harmonics.

The table in figure 4 lists typical

percentages observed for the various

voltage harmonics where:

■ low value = value likely to be found in

the vicinity of large disturbing loads and

associated with a low probability of

having disturbing effects;

■ high value = value rarely exceeded in

the network, and with a higher

probability of having disturbing effects.

typical limits for industrial

networks

It is generally accepted that industrial

network without any sensitive

equipment such as regulators,

programmable controllers, etc. can

accept up to 5 % voltage distortion.

This limit and the limits for the

individual harmonic ratios may be

different if sensitive equipment is

connected to the installation.

harmonic

order

low

value (%)

high

value (%)

2

1

1.5

3

1.5

2.5

4

0.5

1

5

5

6

6

0.2

0.5

7

4

5

8

< 0.2

9

0.8

10

< 0.2

11

2.5

12

< 0.2

13

2

14

< 0.2

15

< 0.3

16

< 0.2

17

1

18

< 0.2

19

0.8

20

< 0.2

21

< 0.2

22

< 0.2

23

0.5

1.5

3.5

3

2

1.5

1

fig. 4: individual voltage harmonic percentages measured in high voltage distribution networks.

Cahier Technique Merlin Gerin n° 152 / p.7

5. harmonics generators

In industrial applications, the main

types equipment that generate

harmonics are:

■ static converters;

■ arc furnaces;

■ lighting;

■ saturated reactors;

■ other equipment, such as rotating

machines which generate slot

harmonics (often negligible).

static converters on

3-phase networks

Rectifier bridges and, more generally,

static converters (made up of diodes

and thyristors) generate harmonics.

A Graetz bridge, for instance, requires

a rectangular pulsed AC current (see

fig. 5) to deliver a perfect DC current. In

spite of their different waveforms, the

currents upstream and downstream

from the delta-star connected

transformer have the same

characteristic harmonic components.

The characteristic harmonic

components of the current pulses

supplying rectifiers have the following

harmonic numbers n, with n = kp ± 1,

where:

■ k = 1, 2, 3, 4, 5...

■ p = number of rectifier arms, for

example:

Graetz bridge

p = 6,

6-pulse bridge

p = 6,

12-pulse bridge

p = 12.

Applying the formula, the p = 6

rectifiers cited above generate

harmonics 5, 7, 11, 13, 17, 19, 23 and

25, and the p = 12 rectifiers generate

harmonics 11, 13, 23 and 25.

The characteristic harmonics are all

odd-numbered and have, as a first

approximation, an amplitude of In = I1/n

where I1 is the amplitude of the

fundamental.

This means that I5 and I7 will have the

greatest amplitudes. Note that they can

be eliminated by using a 12-pulse

bridge (p = 12).

In practice, the current spectrum is

slightly different. New even and odd

harmonics, referred to as non-

Cahier Technique Merlin Gerin n° 152 / p.8

characteristic harmonics, of low

amplitudes, are created and the

amplitudes of the characteristic

harmonics are modified by several

factors including:

■ asymmetry;

■ inaccuracy in thyristor opening times;

■ switching times;

■ imperfect filtering.

For thyristor bridges, a displacement of

the harmonics as a function of the

thyristor phase angle may also be

observed.

Mixed thyristor-diode bridges generate

even harmonics. They are used only at

low ratings because the 2nd harmonic

produces serious disturbances and is

very difficult to eliminate.

Other power converters such as cycloconverters, dimmers, etc. have richer

and more variable spectra than

rectifiers. Note that they are

increasingly replaced by converters

using the PWM (Pulse Width

Modulation) technique. These devices

operate at high chopping frequencies

(20 to 50 kHz) and are generally

designed to generate only low levels of

harmonics.

The harmonic currents of several

converters combine vectorially at the

common supply busbars. Their phases

are generally unknown except for the

case of diode rectifiers. It is therefore

possible to attenuate the 5 th and 7 th

current harmonics using two equally

loaded 6-pulse diode bridges, if the

couplings of the two power supply

transformers are carefully chosen

(see fig. 6).

arc furnaces

Arc furnaces used in the steel industry

may be of the AC (see fig. 7) or

DC type.

AC arc furnaces

(see fig. 7)

The arc is non-linear, asymmetric and

unstable. It generates a spectrum

load

I

I

T

T

t

t

T/6

T/3

rectifier supply phase current

T/6

phase current upstream from a delta-star

connected transformer supplying the rectifier

fig. 5: alternating current upstream from a Graetz bridge rectifier delivering a perfect direct

current.

including odd and even harmonics as

was well as a continuous component

(background noise at all frequencies).

The spectrum depends on the type of

furnace, its power rating and the

operation considered (e.g. melting,

refining). Measurements are therefore

required to determine the exact

spectrum (see fig. 8).

DC arc furnaces

(see fig. 9)

The arc is supplied via a rectifier and is

more stable than the arc in AC furnaces.

The current drawn can be broken down

into:

■ a spectrum similar to that of a

rectifier;

■ a continuous spectrum lower than

that of an AC arc furnace.

To a large extent, the harmonic

currents drawn by the disturbing

equipment are independent of the other

loads and the overall network

impedance. These currents can

therefore be considered to be injected

into the network by the disturbing

equipment. It is simply necessary to

arbitrarily change the sign so that, for

calculation purposes, the disturbing

equipment can be considered as

current sources (see fig. 10).

The approximation is somewhat less

accurate for arc furnaces. In this case,

the current source model must be

corrected by adding a carefully selected

parallel impedance.

in %

In

I1

100

continuous spectrum

10

Lighting systems made up of discharge

lamps or fluorescent lamps are

generators of harmonic currents.

A 3rd harmonic ratio of 25 % is

observed in certain cases. The neutral

conductor then carries the sum of the

3rd harmonic currents of the three

phases, and may consequently be

subjected to dangerous overheating if

not adequately sized.

4

3.2

1.3

1

0.5

0.1

1

3

5

7

9 rang

fig. 8: current spectrum for an arc furnace

supplied by AC power.

HV

I5 and I7 attenuated

lighting

100

transformer

I5 and I7

I5 and I7

cable

Yy 0

Dy 11

rectifier

saturated reactors

The impedance of a saturable reactor is

varying with the current flowing

through it, resulting in considerable

current distortion. This is, for instance,

the case for transformers at no load,

subjected to a continuous overvoltage.

6-pulse

diode

bridge

6-pulse

diode

bridge

cable

load

load

furnace

equal loads

rotating machines

Rotating machines generate high order

slot harmonics, often of negligible

amplitude. However small synchronous

machines generate 3rd order voltage

harmonics than can have the following

detrimental effects:

■ continuous heating (without faults) of

earthing resistors of generator neutrals;

■ malfunctioning of current relays

designed to protect against insulation

faults.

calculation model

When calculating disturbances, static

converters and arc furnaces are

considered to be harmonic current

generators.

fig. 6: attenuation circuit for I5 and I7.

fig. 9: arc furnace supplied by DC power.

HV

transformer

Z

I

cable

furnace

fig. 7: arc furnace supplied by AC power.

fig. 10: harmonic current generators are

modelled as current sources.

Cahier Technique Merlin Gerin n° 152 / p.9

6. can capacitors cause a problem on networks

comprising disturbing equipment?

We will consider the two following

cases:

■ networks without power capacitors;

■ networks with power capacitors.

in the absence of capacitor

banks, harmonic

disturbances are limited

and proportional to the

currents of the disturbing

equipment.

In principle, in so far as are concerned

harmonics, the network remains

inductive.

Its reactance is proportional to the

frequency and, as a first estimate, the

effects of loads and resistance are

negligible. The impedance of the

network, seen from a network node, is

therefore limited to the short-circuit

reactance Xsc at the node considered.

The level of harmonic voltages can be

estimated from the power of the

disturbing equipment and the shortcircuit power at the node (busbars) to

which the disturbing equipment is

connected, the short-circuit reactance

considered to be proportional to the

frequency (see fig. 11).

In figure 11:

Lsc = the short-circuit inductance of the

network, seen from the busbars to

which the disturbing equipment is

connected,

In = currents of the disturbing

equipment,

Xsc n = Lsc ω n = Lsc n (2 π f1)

therefore

V n = Xsc n I n = Lsc n (2 π f1) I n.

The harmonic disturbances generally

remain acceptable as long as the

disturbing equipment does not exceed

a certain power level. However, this

must be considered with caution as

resonance (see the next section) may

be present, caused by a nearby

network possessing capacitors and

coupled via a transformer.

Cahier Technique Merlin Gerin n° 152 / p.10

Note: In reality, the harmonic

inductance of network X, without

capacitors (essentially a distribution

network), represented by Lsc, can only

be considered to be proportional to the

frequency in a rough approximation.

For this reason, the network shortcircuit impedance is generally

multiplied by a factor of 2 or 3 for the

calculations.

Therefore: Xn = k n X1 with k = 2 or 3.

The harmonic impedance of a network

is made up of different constituents

such as the short circuit impedance of

the distribution system as well as the

impedance of the cables, lines,

transformers, distant capacitors,

machines and other loads (lighting,

heating, etc.).

In

Vn

Xsc

I

fig. 11: the harmonic voltage Vn is

proportional to the current In injected by the

disturbing equipment.

node A (busbars)

in the presence of a

capacitor bank parallel

resonance can result in

dangerous harmonic

disturbances

Resonance exists between the

capacitor bank and the reactance of

the network seen from the bank

terminals.

The result is the amplification, with a

varying degree of damping, of the

harmonic currents and voltages if the

order of the resonance is the same as

that of one of the harmonic currents

injected by the disturbing equipment.

This amplified disturbance can be

dangerous to the equipment.

Lsc

I

In

0

a: harmonic electrical

representation of a phase.

E

50 Hz source

Lsc

node A (busbar)

This is a serious problem and will be

dealt with in below.

This phenomenon is referred to as

parallel resonance.

What is this parallel resonance and

how can it cause dangerous

harmonic disturbances?

In so far as harmonic frequencies are

concerned, and for a first

approximation, the network may be

represented as in figure 12.

Vn

load

C

C

load

disturbing equipment

b: single-line diagram.

fig. 12: equivalent diagrams for a circuit

subject to harmonic currents and including a

capacitor bank.

In this diagram:

Lsc = the short-circuit inductance of

the network seen from the busbars to

which the capacitor bank and the

disturbing equipment are connected,

C = capacitors,

In = currents of the disturbing

equipment,

load = loads (Joule effect,

transmission of mechanical energy).

In principle, we consider the shortcircuit harmonic reactance seen from

the busbars, i.e. the node (A) to which

the capacitors, the loads and the

disturbing equipment are connected,

giving Vn = ZAO In.

The impedance versus frequency

curves (see fig.13) show that:

■ for the resonance frequency far, the

inductive effect is compensated for

exactly by the capacitive effect;

■ the reactance of the rejecter circuit:

is inductive for low frequencies,

including the fundamental frequency,

increases with frequency, becoming

very high and suddenly capacitive at

the resonance frequency far;

■ the maximum impedance value

reached is roughly R = U2/P where P

represents the sum of the active power

values of the loaded motors, other than

those supplied by a static converter.

If a harmonic current In of order n , with

the same frequency as the parallel

resonance frequency far, is injected by

the disturbing equipment, the

corresponding harmonic voltage can be

estimated as Vn = R In

with n = n ar = f ar/f1.

Estimation of nar

The order nar of parallel resonance is

the ratio of the resonance frequency far

to the fundamental frequency f1 (power

frequency).

Consider the most elementary industrial

network, shown in the equivalent

diagram in figure 14, including a

capacitor bank C supplied by a

transformer with a short-circuit

inductance LT, where Lsc represents

the short-circuit inductance of the

distribution network seen from the

upstream terminals of the transformer,

f ar =

2π

1

.

(Lsc + L T ) C

The order of the parallel resonance is

roughly the same whether the network

impedance is seen from point A or

point B (e.g. the supply terminals).

In general, given the short-circuit power

at the capacitor bank terminals,

and undoubtedly present a danger to

the capacitors.

■ if the parallel resonance order

corresponds to the frequency of the

carrier-current control equipment of the

power distribution utility, there is a risk

of disturbing this equipment.

Ssc

Q

nar =

To prevent resonance from

becoming dangerous, it must be

forced outside the injected spectrum

and/or damped.

The short-circuit impedance of the

network is seldom accurately known

and, in addition, it can vary to a large

extent, thereby resulting in large

variations of the parallel resonance

frequency.

It is therefore necessary to stabilise this

frequency at a value that does not

correspond to the frequencies of the

injected harmonic currents. This is

achieved by connecting a reactor in

series with the capacitor bank.

where:

Ssc = short-circuit power at the

capacitor bank terminals,

Q = capacitor bank power at the

applied voltage.

Generally S is expressed in MVA and

Q in Mvar.

Practical consequences:

■ if the order of a harmonic current

injected by disturbing equipment

corresponds to the parallel resonance

order, there is a risk of harmonic

overvoltages, especially when the

network is operating at low loads. The

harmonic currents then become

intensively high in network constituents

XΩ

IZI Ω

~R

without capacitors

X = Lsc 2 π f

inductive

0

f (Hz)

without capacitors

IZI = Lsc 2 π f

0

f (Hz)

far

capacitive

far

fig. 13: curves showing the impedance due to the loads and due to the resistance of the

conductors.

B

A

LT

lopp

distributor

Lsc

load

C

I

0

fig. 14: the capacitor, together with the sum of the upstream impedances, forms a resonant

circuit.

Cahier Technique Merlin Gerin n° 152 / p.11

The rejecter circuit thus created is then

represented by the diagram in figure 15

where Vn = ZAO In.

A series resonance, between L and C,

appears. As opposed to this resonance,

which gives a minimum impedance, the

parallel resonance is often referred to

an anti-resonance.

The equation giving the frequency of

the anti-resonance is:

f ar =

1

(Lsc + L) C

2π

Lsc generally being small compared to

L, the equation shows that the

presence of reactor L, connected in

series with the capacitors, renders the

frequency far less sensitive to the

variations of the short-circuit inductance

Lsc (from the connections points =

busbars A).

Series resonance

The branch made up of reactor L and

capacitor C (see fig. 16), form a series

resonance system of impedance

Z = r + j(Lω - 1/Cω) with:

■ a minimum resistive value r

(resistance of the inductance coil) for

the resonance frequency fr;

■ a capacitive reactance below the

resonance frequency fr;

■ an inductive reactance above the

resonance frequency fr, where

fr =

1

2π

L C

.

The curves in figure 17 show the shape

of the network inductance, including the

short-circuit impedance and that of the

LC branch, seen from busbars A.

The choice of far depends on Lsc, L

and C, while that of fr depends only on

L and C; far and fr therefore become

closer as Lsc becomes small with

respect to L. The level of reactive

power compensation, and the voltage

applied to the capacitors, depend partly

on L and C.

The reactor L can be added in two

different manners, depending on the

position of the series resonance with

respect to the spectrum. The two forms

of equipment are:

■ anti-harmonic reactors (for series

resonance outside the spectrum lines);

■ filters (for series resonance on a

spectrum line).

XΩ

inductive

0

XΩ

ph1

f (Hz)

capacitive

inductive

fr

0

r

f (Hz)

far

capacitive

fr

busbar node, point A

IZIΩ

L

IZIΩ

L

Vn

Lsc

I

In

C

0

neutral

C

0

~r

r

f (Hz)

0

fig. 15: the reactor, connected in series with

the capacitor, forms a rejecter circuit.

Cahier Technique Merlin Gerin n° 152 / p.12

f (Hz)

fr

fig. 16: impedance of the rejecter circuit.

far

fig. 17: network impedance at point A.

fr

7. anti-harmonic reactors

An anti-harmonic reactor can be used

to protect a capacitor bank against

harmonic overloads. Such solutions are

often referred to as reactor-connected

capacitor installations.

The reference diagram is once again

figure 15.

In this assembly, the choice of L is such

that the LC branch (where L is the

reactor and C the reactive power

compensation capacitors) behaves

inductively for the harmonic

frequencies, over the spectrum.

As a result, the resonance frequency fr

of this branch will be below the

spectrum of the disturbing equipment.

The LC branch and the network (Lsc)

are then both inductive over the

spectrum and the harmonic currents

injected by the disturbing equipment

are divided in a manner inversely

proportional to the impedance.

Harmonic currents are therefore greatly

restricted in the LC branch, protecting

the capacitors, and the major part of

the harmonic currents flow in the rest of

the network, especially in the shortcircuit impedance.

The shape of the network impedance,

seen from the busbars to which the LC

branch is connected, is shown in

figure 18.

There is no anti-resonance inside the

current spectrum. The use of an antiharmonic reactor therefore offers two

advantages;

■ it eliminates the danger of high

harmonic currents in the capacitors;

■ it correlatively eliminates the high

distortions of the network voltage,

without however lowering them to a

specified low value.

Certain precautions are necessary:

■ no other capacitor banks must be

present that could induce, through antiresonance, a capacitive behaviour in

the initial network inside the spectrum;

■ care must be taken not to introduce

an anti-resonance with a frequency

used by the distribution utility for

carrier-current control, since this would

place an increased load on the high

frequency generators (175 Hz, 188 Hz).

The anti-harmonic reactor is tuned to

an order of 4.5 to 4.8, giving a value

of fr between 225 to 240 Hz for a

50 Hz network, which is very near the

ripple control frequency used on many

distribution networks;

■ due to the continuous spectrum, the

use of anti-harmonic reactors on arc

furnaces requires certain precautions

which can only be defined after carrying

out special studies.

IzIΩ

theoretical impedance without

the LC branch

f (Hz)

f1

fr

harmonic current

spectrum

far

fig. 18: the capacitors are protected when fr is well below the harmonic spectrum.

Cahier Technique Merlin Gerin n° 152 / p.13

8. filters

Filters are used when it is necessary to

limit harmonic voltages present on a

network to a specified low value. Two

types of filters may be used to reduce

harmonic voltages:

■ resonant shunt filters,

■ damped filters.

resonant shunt filters

The resonant shunt filter (see fig. 16) is

made up of an LC branch with a

frequency of

fr =

1

2π L C

tuned to the frequency of the voltage

harmonic to be eliminated.

This approach is therefore

fundamentally different than that of

reactor-connected capacitors

already described. At fr, the resonant

shunt presents a low minimum

impedance with respect to the

resistance r of the reactor. It therefore

absorbs nearly all the harmonic

currents of frequency fr injected, with

low harmonic voltage distortion (since

proportional to the product of the

resistance r and the current flowing in

the filter) at this frequency.

In principle, a resonant shunt is

installed for each harmonic to be

limited. They are connected to the

busbars for which harmonic voltage

reduction is specified. Together they

form a filter bank.

Figure 19 shows the harmonic

impedance of a network equipped with

a set of four filters tuned to the 5th, 7th,

11th and 13th harmonics. Note that

there are as many anti-resonances as

there are filters. These anti-resonances

must be tuned to frequencies between

the spectrum lines. A careful study must

therefore be carried out if it is judged

necessary to segment the filter bank.

Main characteristics of a resonant

shunt

The characteristics depend on

n r = fr/f1 the order of the filter tuning

frequency, with:

■ fr = tuning frequency;

■ f1 = fundamental frequency (generally

the power frequency, e.g. 50 Hz).

These characteristics are:

■ the reactive power for compensation:

Qvar.

The resonant shunt, behaving

capacitively below its tuning frequency,

contributes to the compensation of

reactive power at the power frequency.

The reactive power produced by the

shunt at the connection busbars, for an

operating voltage U1, is given by the

following equation:

Q var =

nr2

n12 −

U12 C 2π f1

n

(note that the subscript 1 refers to the

fundamental).

C is the phase-to-neutral capacitance

of one of the 3 branches of the filter

bank represented as a star.

At first glance, the presence of a

reactor would not be expected to

increase the reactive power supplied.

The reason is the increase in voltage at

power frequency f1 caused by the

inductance at the capacitor terminals;

■

characteristic impedance:

L

;

C

X0 =

the quality factor:

q = X0/r.

An effective filter must have a reactor

with a large quality factor q, therefore:

r << X0 at frequency fr.

Approximate values of q:

75 for air-cored reactors,

greater than 75 for iron-core reactors.

■ the pass-band (see fig. 20), in relative

terms:

■

PB =

f − fr

1

= 2

fr

q

=

r

;

X0

the resistance of the reactor:

r = X0/q.

This resistance is defined at

frequency fr.

It depends on the skin effect. It is also

the impedance when the resonant

shunt is tuned;

■ the losses due to the capacitive

current at the fundamental frequency:

■

p1 =

Q var

q nr

IZIΩ

IZIΩ

r

2

r

f

fr

1

5

7

fig. 19: impedance of a network equipped with shunt filters.

Cahier Technique Merlin Gerin n° 152 / p.14

11

13

f/f1

fig. 20: Z versus f curve for a resonant

shunt.

f (Hz)

with:

Qvar = reactive power for

compensation produced by the filter,

p1 = filter losses at power frequency

in W;

■ the losses due to the harmonic

currents cannot be expressed by simple

equations; they are greater than:

pn =

2

Unr

r

in which Unr is the phase-to-phase

harmonic voltage of order nr on the

busbars after filtering.

In practice, the performance of

resonant shunt filters is reduced by

mis-tuning and special solutions are

required as follows:

■ adjustment possibilities on the

reactors for correction of manufacturing

tolerances;

■ a suitable compromise between the q

factor and filter performance to reduce

the sensitivity to mis-tuning, thereby

accepting fluctuations of f1 (network

frequency) and fr (caused by the

temperature dependence of the

capacitance of the capacitors).

damped filters

2nd order damped filter

On arc furnaces, the resonant shunt

must be damped. This is because the

continuous spectrum of an arc furnace

increases the probability of an injected

current with a frequency equal to the

anti-resonance frequency. In this case, it

is no longer sufficient to reduce the

characteristic harmonic voltages. The

anti-resonance must also be diminished

by damping.

Moreover, the installation of a large

number of resonant shunts is often

costly, and it is therefore better to use a

wide-band filter possessing the following

properties:

■ anti-resonance damping;

■ reduced harmonic voltages for

frequencies greater than or equal to its

tuning frequency, leading to the name

«damped high-pass filter»;

■ fast damping of transients produced

when the filter is energised. The 2nd

order damped filter is made up of a

resonant shunt with a damping

resistor R added at the reactor

terminals. Figure 21 shows one of the

three phases of the filter.

The 2nd order damped filter has zero

reactance for a frequency fr higher than

the frequency f where:

f =

fr =

2π

1

and

L C

1+ Q q

2π q

(Q 2 − 1) L C

.

The filter is designed so that fr

coincides with the first characteristic

line of the spectrum to be filtered. This

line is generally the largest.

When Q (or R) take on high values, fr

tends towards f, which means that the

resonant shunt is a limiting case of the

2nd order damped filter.

It is important not to confuse Q, the

quality factor, with Qvar, the reactive

power of the filter for compensation.

The 2nd order damped filter operates

as follows:

■ below fr: the damping resistor

contributes to the reduction of the

network impedance at anti-resonance,

thereby reducing any harmonic

voltages;

■ at fr: the reduction of the harmonic

voltage to a specified value is possible

since, at this frequency, no resonance

can occur between the network and the

filter, the latter presenting an

impedance of a purely resistive

character.

However, this impedance being higher

than the resistance r of the reactor, the

filtering performance is less than for a

resonant shunt;

■ above fr: the filter presents an

inductive reactance of the same type as

the network (inductive), which lets it

adsorb, to a certain extent, the

spectrum lines greater than fr, and in

particular any continuous spectrum that

may be present. However, antiresonance, if present in the impedance

of the network without the filter, due to

the existing capacitor banks, reduces

the filtering performance. For this

reason, existing capacitor banks must

be taken into account in the design of

the network and, in some cases, must

be adapted.

The main electrical characteristics of a

2nd order damped filter depend on

n r = fr/f1 , the order of the filter tuning

frequency, with:

■ fr = tuning frequency;

■ f1 = fundamental frequency (generally

the power frequency, e.g. 50 Hz).

These characteristics are:

■ the reactive power for compensation:

For a 2nd order damped filter at

operating voltage U1 (the subscript 1

referring to the fundamental), the

reactive power is roughly the same as

for a resonant shunt with the same

inductance and capacitance, i.e. in

practice:

Q var =

nr2

2

nr − 1

U12 C 2π f1

C is the phase-to-neutral capacitance of

one of the 3 branches of the filter bank

represented as a star.

phase

XΩ

r

inductive

0

R

f (Hz)

L

capacitive

C

neutral

fr

f =

1

2π

L C

fig. 21: 2nd order damped filter.

Cahier Technique Merlin Gerin n° 152 / p.15

■

characteristic impedance:

X0 =

phase

L

;

C

the quality factor of the reactor:

q = X0/r

where r is the resistance of the reactor,

dependent on the skin effect and

defined at frequency fr;

■ the quality factor of the filter:

Q = R/X0.

The quality factors Q used are

generally between 2 and 10;

■ the losses due to the fundamental

compensation current and to the

harmonic currents; these are higher

than for a resonant shunt and can only

be determined through network

analysis.

The damped filter is used alone or in a

bank including two filters. It may also

be used together with a resonant shunt,

with the resonant shunt tuned to the

lowest lines of the spectrum.

Figure 22 compares the impedance of

a network with a 2nd order damped

filter to that of a network with a

resonant shunt.

■

Other types of damped filters

Although more rarely used, other

damped filters have been derived from

the 2nd order filter:

■ 3rd order damped filter (see fig. 23)

Of a more complex design than the 2nd

order filter, the 3rd order filter is

intended particularly for high

compensation powers.

The 3rd order filter is derived from a 2nd

order filter by adding another capacitor

bank C2 in series with the resistor R,

thereby reducing the losses due to the

fundamental.

C2 can be chosen to improve the

behaviour of the filter below the tuning

frequency as well, which favours the

reduction of anti-resonance.

The 3rd order filter should be tuned to

the lowest frequencies of the spectrum.

Given the complexity of the 3rd order

filter, and the resulting high cost, a 2nd

order filter is often preferred for

industrial applications;

■ type C damped filter (see fig. 24)

In this filter, the additional capacitor

bank C2 is connected in series with the

reactor. This filter offers characteristics

roughly the same as those of the 3rd

order filter;

Cahier Technique Merlin Gerin n° 152 / p.16

IZIΩ

r

with resonant shunt

R

Z

network

L

with 2nd order damped filter

C

f (Hz)

neutral

fig. 22: the impedance, seen from point A, of a network equipped with either a 2nd order

damped filter or a resonant shunt.

phase

phase

r

r

R

R

L

L

C2

C2

C

C

neutral

fig. 23: 3rd order damped filter.

■ damped double filter (see fig. 25)

Made up of two resonant shunts

connected by a resistor R, this filter is

specially suited to the damping of the

anti-resonance between the two tuning

frequencies;

low q resonant shunt

This filter, which behaves like a

damped wide-band filter, is designed

especially for very small installations

not requiring reactive power

compensation.

The reactor, with a very high

resistance (often due to the addition of

a series resistor) results in losses

which are prohibitive for industrial

applications.

neutral

fig. 24: type C damped filter.

phase

ra

rb

La

Lb

■

R

Cb

Ca

neutral

neutral

fig. 25: damped double filter.

9. measurement relays required for the protection of

reactor-connected capacitors and filters

An anti-harmonic reactor must

withstand the 3-phase short-circuit

current at the common reactorcapacitor terminals.

Furthermore, both anti-harmonic

reactors and filters must continuously

withstand fundamental and harmonic

currents, fundamental and harmonic

voltages, switching surges and

dielectric stresses.

In this chapter, anti-harmonic reactorconnected capacitor assemblies and

filters will be referred to collectively as

«devices».

basic protection against

device failures

All the elements of these devices can

be subject to insulation faults and shortcircuits, while the capacitor banks are

mainly the source of unbalance faults

caused by the failure of capacitor

elements.

■ protection of these devices against

insulation faults can be provided by

residual current relays (or zero phase

sequence relays).

Note:

the neutral is generally not distributed

on such devices;

for higher sensing accuracy, it is

better to use a toroidal type

transformer, encircling all the live

conductors of the feeder, rather than

three step-down current transformers;

■ protection against short-circuits can

be provided by overcurrent relays

installed on the «filter» feeder.

This protection must detect 2-phase

short-circuits at the common reactorcapacitor terminals, while letting

through inrush transients;

■ detection of unbalance currents in the

connections between the neutrals of

the double star connected capacitor

banks (see fig. 26).

In addition to the damage that can be

caused by the resulting unbalanced

stresses, the failure of a small number

of capacitor elements is detrimental to

filter performance.

This protection is therefore designed to

detect, depending on its sensitivity, the

failure of a small number of capacitor

elements. Of the single-pole type, this

protection must be:

insensitive to the harmonics,

set to above the natural unbalance

current of the double star connected

capacitor bank (this unbalance depends

on the accuracy of the capacitors),

set to below the unbalance current

due to the failure of a single capacitor

element,

operate on a major fault causing an

unbalance.

The fluctuation of the supply voltage

must be taken into account in the

calculation of all these currents.

basic protection against

abnormal stresses on the

devices

These abnormal stresses are

essentially due to overloads. To protect

against them, it is necessary to monitor

the rms value of the distorted current

(fundamental and harmonics) flowing in

the filter.

It is also necessary to monitor the

fundamental voltage of the power

supply using an overvoltage relay.

phase 1

current relay

C/2

phase 2

phase 3

r

r

r

L

L

L

C/2

C/2

C/2

C/2

C/2

fig. 26: unbalance detection for a double star connected capacitor bank.

Cahier Technique Merlin Gerin n° 152 / p.17

10. example of the analysis of a simplified network

The diagram in figure 27 represents a

simplified network comprising a

2,000 kVA six-pulse rectifier, injecting a

harmonic current spectrum, and the

following equipment which will be

considered consecutively in three

different calculations:

■ a single 1,000 kvar capacitor bank;

■ anti-harmonic reactor-connected

capacitor equipment rated 1000 kvar;

■ a set of two filters comprising a

resonant shunt tuned to the 5th

harmonic and a 2nd order damped filter

tuned to the 7th harmonic. The

capacitor bank implemented in this

manner is rated 1,000 kvar.

Note that:

■ the 1,000 kvar compensation power

is required to bring the power factor to

a conventional value;

■ the harmonic voltages already

present on the 20 kV distribution

network have been neglected for the

sake of simplicity.

This example will be used to compare

the performance of the three solutions,

however the results can obviously not

be applied directly to other cases.

capacitor bank alone

The network harmonic impedance

curve (see fig. 28), seen from the node

where the harmonic currents are

injected, exhibits a maximum (antiresonance) in the vicinity of the

7th current harmonic. This results in an

unacceptable individual harmonic

voltage distortion of 11 % for the 7th

harmonic (see fig. 29).

The following characteristics are also

unacceptable:

■ a total harmonic voltage distortion of

12.8 % for the 5.5 kV network,

compared to the maximum permissible

value of 5 % (without considering the

requirements of special equipment);

■ a total capacitor load of 1.34 times

the rms current rating, exceeding the

permissible maximum of 1.3

(see fig. 30).

The solution with capacitors alone is

therefore unacceptable.

Cahier Technique Merlin Gerin n° 152 / p.18

The network harmonic impedance

curve, seen from the node where the

harmonic currents are injected, exhibits

a maximum of 16 ohms (antiresonance) in the vicinity of

harmonic order 4.25. This unfortunately

favours the presence of 4th voltage

reactor-connected

capacitor bank

This equipment is arbitrarily tuned to

4.8 f1.

Harmonic impedance

(see fig. 31)

network

20 kV

Isc 12.5 kA

2,000 kVA

disturbing equipment

20/5.5 kV

5,000 kVA

Usc 7.5 %

Pcu 40 kW

5.5/0.4 kV

1,000 kVA

Usc 5 %

Pcu 12 kW

capa.

motor

load

reactor

+

capa.

560 kW

resonant shunt

and

2nd order damped filter

500 kVA at cos ϕ = 0.9

fig. 27: installation with disturbing equipment, capacitors and filters.

Z (Ω)

V (V)

38.2

350

11 %

7.75

H

fig. 28: harmonic impedance seen from the

node where the harmonic currents are

injected in a network equipped with a

capacitor bank alone.

3

5

7

8

9 10 11 13 H

fig. 29: harmonic voltage spectrum of a

5.5 kV network equipped with a capacitor

bank alone.

harmonic. However, the low

impedance, of an inductive character,

of the 5th harmonic favours the filtering

of the 5th harmonic quantities.

For the 20 kV network, the total

harmonic distortion is only 0.35 %, an

acceptable value for the distribution

utility.

Voltage distortion

(see fig. 32)

For the 5.5 kV network, the individual

harmonic voltage ratios of 1.58 %

(7th harmonic), 1.5 % (11th harmonic)

and 1.4 % (13th harmonic) may be too

high for certain loads. However in many

cases the total harmonic voltage

distortion of 2.63 % is acceptable.

Capacitor current load

(see fig. 33)

The total rms current load of the

capacitors, including the harmonic

currents, is 1.06 times the current rating,

i.e. less than the maximum of 1.3.

This is the major advantage of reactorconnected capacitors compared to the

first solution (capacitors alone).

I (A)

V (V)

50

1.55 %

- 82

48

1.5 % 45

1.4 %

19

0.6 %

3

5

7

8

9 10 11 13

fig. 30: spectrum of the harmonic currents

flowing in the capacitors for a network

equipped with a capacitor bank alone.

Z (Ω)

3

H

4

5

7

8

9

11 13 H

fig. 32: harmonic voltage spectrum of a

5.5 kV network equipped with reactorconnected capacitors.

resonant shunt filter tuned

to the 5th harmonic and a

damped filter tuned to the

7th harmonic

In this example, the distribution of the

reactive power between the two filters

is such that the filtered 5th and 7th

voltage harmonics have roughly the

same value. In reality, this is not

required.

Harmonic impedance

(see fig. 34)

The network harmonic impedance

curve, seen from the node where the

harmonic currents are injected, exhibits

a maximum of 9.5 ohms (antiresonance) in the vicinity of

harmonic 4.7.

For the 5th harmonic, this impedance is

reduced to the reactor resistance,

favouring the filtering of the 5th

harmonic quantities.

For the 7th harmonic, the low, purely

resistive impedance of the damped

filter also reduces the individual

harmonic voltage.

For harmonics higher than the tuning

frequency, the damped filter impedance

curve reduces the corresponding

harmonic voltages.

This equipment therefore offers an

improvement over the second solution

(reactor-connected capacitors).

I (A)

15.6

Z (Ω)

9.5

34

24 %

4.7

~ 4.25

4.8

H

fig. 31: harmonic impedance seen from the

node where the harmonic currents are

injected in a network equipped with reactorconnected capacitors.

5

7

11 13

H

fig. 33: spectrum of the harmonic currents

flowing in the capacitors for a network

equipped with reactor-connected

capacitors.

5

7

H

fig. 34: harmonic impedance seen from

the node where the harmonic currents

are injected in a network equipped with a

resonant shunt filter tuned to the

5th harmonic and a damped filter

tuned to the 7th harmonic.

Cahier Technique Merlin Gerin n° 152 / p.19

Voltage distortion

(see fig. 35)

For the 5.5 kV network, the individual

harmonic voltage ratios of 0.96 %,

0.92 %, 1.05 % and 1 % for the 5th,

7th, 11th and 13th harmonics

respectively are acceptable for most

sensitive loads. The total harmonic

voltage distortion is 1.96 %.

For the 20 kV network, the total

harmonic distortion is only 0.26 %, an

acceptable value for the distribution

utility.

Capacitor current load

The total rms current load of the

resonant shunt filter capacitors

(see fig. 36) is greater than 1.3 time the

current rating. The capacitance must

therefore be increased, which will

improve the filtering performance,

reducing the 5th harmonic ratio to less

than 1 %.

The result is of course an increase in

the reactive power compensation

capacity.

To avoid overcompensating, a compromise must be found for the size of

these capacitors. The calculation is

therefore repeated with this new data.

For the damped filter tuned to the 7th

harmonic, the total rms current load of

the capacitors (see fig. 37) is within the

tolerance of 1.3 times their current

rating.

This example demonstrates an initial

approach to the problem. However in

practice, over and above the

calculations relative to the circuit

elements (L, r, C and R), other

calculations are required before

I (A)

V (V)

0.96 %

0.91 %

1.05 %

1%

proceeding with the implementation of

any solution:

■ the spectra of the currents flowing in

the reactors connected to the

capacitors;

■ the total voltage distortion at the

capacitor terminals;

■ reactor manufacturing tolerances and

means for adjustment if necessary;

■ the spectra of the currents flowing in

the resistors of the damped filters and

their total rms value;

■ voltage and energy transients

affecting the filter elements during

energisation.

These more difficult calculations,

requiring a solid understanding of both

the network and the equipment, are

used to determine all the electrotechnical information required for the

filter manufacturing specifications.

I (A)

22

23 %

39

10

10 %

5

7

11 13

H

fig. 35: harmonic voltage spectrum of a

5.5 kV network equipped with a

resonant shunt filter tuned to the 5th

harmonic and a damped filter tuned to

the 7th harmonic.

Cahier Technique Merlin Gerin n° 152 / p.20

5

H

fig. 36: spectrum of the harmonic currents

flowing in the capacitors of a resonant shunt

filter tuned to the 5th harmonic on a network

equipped with a damped filter tuned to the

7th harmonic.

5

7

11 13

H

fig. 37: spectrum of the harmonic currents

flowing in the capacitors of a damped filter

tuned to the 7th harmonic on a network

equipped with a resonant shunt filter tuned

to the 5th harmonic.

11. conclusion

Static power converters are

increasingly used in industrial

distribution. The same is true for arc

furnaces in the growing electricpowered steel industry. All these loads

produce harmonic disturbances and

require compensation of the reactive

power they consume, leading to the

installation of capacitor banks.

Unfortunately these capacitors, in

conjunction with the inductances in the

network, can cause high frequency

oscillations that amplify harmonic

disturbances. Installers and operators

of industrial networks are thus often

confronted with a complex electrical

problem.

acquired experience, this document

should provide the necessary

background to, if not solve the

problems, at least facilitate discussions

with specialists.

The main types of harmonic

disturbances and the technical means

available to limit their extent have been

presented in this document. Without

offering an exhaustive study of the

phenomena involved or relating all

For further information or assistance,

feel free to contact the Network Studies

department of the Central R&D organisation of Merlin Gerin, a group of

specialised engineers with more than

twenty years of experience in this field.

Cahier Technique Merlin Gerin n° 152 / p.21

12. bibliography

Standards

■ IEC 146: Semi-conductor converters.

■ IEC 287: Calculation of the

continuous current rating of cables.

■ IEC 555-1: Disturbances in supply

systems caused by household

appliances and similar electrical

equipment - Definitions.

■ IEC 871-1 and HD 525.1-S-T:

Shunt capacitors for AC power systems

having a rated voltage above 660 V.

■ NF C 54-100.

■ HN 53 R01 (May 1981): EDF general

orientation report. Particular aspects

concerning the supply of electrical

power to sensitive electronic equipment

and computers.

Merlin Gerin's Cahier Technique

■ Residual current devices

Cahier Technique n° 114

R. CALVAS

■ Les perturbations électriques en BT

Cahier Technique n° 141

R. CALVAS

Other publications

■ Direct current transmission, volume 1

E. W. KIMBARK

published by: J. WILEY and SONS.

Le cyclo-convertisseur et ses

influences sur les réseaux

d'alimentation (The cyclo-converter and

its effects on power supply networks

T. SALZAM and W. SCHULTZ - AIM

Liège CIRED 75.

■

Perturbations réciproques des

équipements électroniques de

puissance et des réseaux - Quelques

aspects de la pollution des réseaux par

les distorsions harmoniques de la

clientèle (Mutual disturbances between

power electronics equipment and

networks - Several aspects concerning

network pollution by harmonic distortion

produced by subscribers).

Michel LEMOINE - DER EDF

RGE T 85 n° 3 03/76.

■

Cahier Technique Merlin Gerin n° 152 / p.22

■ Perturbations des réseaux industriels

et de distribution. Compensation par

procédés statistiques.

Résonances en présence des

harmoniques créés par les

convertisseurs de puissance et les

fours à arc associés à des dispositifs

de compensation.

(Disturbances on industrial and

distribution networks. Compensation by

statistical processes.

Resonance in the presence of

harmonics created by power converters

and arc furnaces associated with

compensation equipment.)

Michel LEMOINE - DER EDF

RGE T 87 n° 12 12/78.

■ Perturbations des réseaux industriels

et de distribution. Compensation par

procédés statistiques.

Perturbations de tension affectant le

fonctionnement des réseaux fluctuations brusques, flicker,

déséquilibres et harmoniques.

(Disturbances on industrial and

distribution networks. Compensation by

statistical processes.

Voltage disturbances affecting network

operation - fluctuations, flicker,

unbalances and harmonics.

M. CHANAS - SER-DER EDF

RGE T 87 n° 12 12/78.

■ Pollution de la tension

(Voltage disturbances).

P. MEYNAUD - SER-DER EDF

RGE T 89 n° 9 09/80.

■ Harmonics, characteristic

parameters, methods of study,

estimates of existing values in the

network.

(ELECTRA) CIGRE 07/81.

■ Courants harmoniques dans les

redresseurs triphasés à commutation

forcée.

(Harmonic currents in forced

commutation 3-phase rectifiers)

W. WARBOWSKI

CIRED 81.

Origine et nature des perturbations

dans les réseaux industriels et de

distribution.

(Origin and nature of disturbances in

industrial and distribution networks).

Guy BONNARD - SER-DER-EDF

RGE 1/82.

■ Problèmes particuliers posés par

létude du phénomène de distorsion

harmonique dans les réseaux.

(Particular problems posed by the study

of harmonic distortion phenomena in

networks).

P. REYMOND

CIGRE Study Committee 36 09/82.

■ Réduction des perturbations

électriques sur le réseau avec le four à

arc en courant continu (Reduction of

electrical network disturbances by DC

arc furnaces).

G. MAURET, J. DAVENE

IRSID SEE LYON 05/83.

■ Line harmonics of converters with DC

motor loads.

A. DAVID GRAHAM and EMIL T.

SCHONHOLZER.

IEEE transactions on industry

applications.

Volume IA 19 n° 1 02/83.

■ Filtrage dharmoniques et

compensation de puissance réactive Optimisation des installations de

compensation en présence

d'harmoniques.

(Harmonic filtering and reactive power

compensation - Optimising

compensation installations in the

presence of harmonics).

P. SGARZI and S. THEOLERE,

SEE Seminar RGE n° 6 06/88.

■

Cahier Technique Merlin Gerin n° 152 / p.23

Réal. : Illustration Technique Lyon -

Cahier Technique Merlin Gerin n° 152 / p.24

DTE - 10/94 - 2500 - Imprimeur :